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Published online by Cambridge University Press:  05 June 2012

Richard E. Blahut
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University of Illinois, Urbana-Champaign
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Print publication year: 2003

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References

Abramson, N. A., Class of Systematic Codes for Non-Independent Errors, IRE Transactions on Information Theory, vol. IT-5, pp. 150–157, 1959CrossRefGoogle Scholar
Abramson, N. A., A Note on Single Error-Correcting Binary Codes, IRE Transactions on Information Theory, vol. IT-6, pp. 502–503, 1960CrossRefGoogle Scholar
V. I. Andryanov and V. N. Saskovets, Decoding Codes, Akad. Nauk. Ukr. SSR Kibernetika, Part 1, 1966
Arimoto, S., Encoding and Decoding of p-ary Group Codes and the Correction System (in Japanese), Information Processing in Japan, vol. 2, pp. 321–325, 1961Google Scholar
Assmus, E. F. Jr and Mattson, H. F. Jr, Coding and Combinatorics, SIAM Review, vol. 16, pp. 349–388, 1974CrossRefGoogle Scholar
E. F. Assmus, Jr., H. F. Mattson, Jr., and R. J. Turyn, Cyclic Codes, AFCRL-65–332, Air Force Cambridge Research Labs, Bedford, MA, 1965
Baggen, C. P. M. J. and Tolhuizen, L. M. G. M., On Diamond Codes, IEEE Transactions on Information Theory, vol. IT-43, pp. 1400–1411, 1997CrossRefGoogle Scholar
Bahl, L. R. and Jelinek, F., Rate 1/2 Convolutional Codes with Complementary Generators, IEEE Transactions on Information Theory, vol. IT-17, pp. 718–727, 1971CrossRefGoogle Scholar
Bahl, L. R., Cocke, J., Jelinek, F., and Raviv, J., Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate, IEEE Transactions on Information Theory, vol. IT-20, pp. 284–287, 1974CrossRefGoogle Scholar
Bartee, T. C. and Schneider, D. I., Computation with Finite Fields, Information and Control, vol. 6, pp. 79–98, 1963CrossRefGoogle Scholar
Bassalygo, L. A., New Upper Bounds for Error Correcting Codes, Problemy Peredachi Informatsii, vol. 1, pp. 41–45, 1965Google Scholar
B. Baumslag and B. Chandler, Theory and Problems of Group Theory, Schaum's Outline Series, McGraw-Hill, New York, NY, 1968
Berlekamp, E. R., The Enumeration of Information Symbols in BCH Codes, Bell System Technical Journal, vol. 46, pp. 1861–1880, 1967CrossRefGoogle Scholar
E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, NY, 1968
Berlekamp, E. R., Long Primitive Binary BCH Codes Have Distanced ∼ 2n ln R−1log n …, IEEE Transactions on Information Theory, vol. IT-18, pp. 415–416, 1972CrossRefGoogle Scholar
Berlekamp, E. R., Bit Serial Reed–Solomon Encoders, IEEE Transactions on Information Theory, vol. IT-28, pp. 869–874, 1982CrossRefGoogle Scholar
Berrou, C. and Glavieux, A., Near Optimum Error Correcting Coding and Decoding: Turbo-Codes, IEEE Transactions on Communications, vol. COM-44, pp. 1261–1271, 1996CrossRefGoogle Scholar
C. Berrou, A. Glavieux, and P. Thitimajshima, Near Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes, Proceedings of the IEEE International Conference on Communications, Geneva, Switzerland, IEEE, Piscataway, NJ, 1993
G. Birkhoff and S. MacLane, A Survey of Modern Algebra, Revised Edition, Macmillan, New York, NY, 1953
R. E. Blahut, Algebraic decoding in the frequency domain, in Algebraic Coding Theory and Practice, G. Longo, editor, Springer-Verlag, New York, NY, 1979
Blahut, R. E., Transform Techniques for Error-Control Codes, IBM Journal of Research and Development, vol. 23, pp. 299–315, 1979CrossRefGoogle Scholar
R. E. Blahut, On Extended BCH Codes, Proceedings of the Eighteenth Annual Allerton Conference on Communication, Control, and Computers, pp. 50–59, University of Illinois, Monticello, IL, 1980
Blahut, R. E., A Universal Reed–Solomon Decoder, IBM Journal of Research and Development, vol. 28, pp. 150–158, 1984CrossRefGoogle Scholar
R. A. Blum and A. D. Weiss, Further Results in Error-Correcting Codes, S.M. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1960
Bose, R. C. and Ray-Chaudhuri, D. K., On a Class of Error-Correcting Binary Group Codes, Information and Control, vol. 3, pp. 68–79, 1960CrossRefGoogle Scholar
Burton, H. O., Inversionless Decoding of Binary BCH Codes, IEEE Transactions on Information Theory, vol. IT-17, pp. 464–466, 1971CrossRefGoogle Scholar
Burton, H. O. and Weldon, E. J. Jr, Cyclic Product Codes, IEEE Transactions on Information Theory, vol. IT-11, pp. 433–439, 1965CrossRefGoogle Scholar
Bussgang, J. J., Some Properties of Binary Convolutional Code Generators, IEEE Transactions on Information Theory, vol. IT-11, pp. 90–100, 1965CrossRefGoogle Scholar
Calderbank, A. R., Forney, G. D. Jr, and Vardy, A., Minimal Tail-Biting Trellis: The Golay Code and More, IEEE Transactions on Information Theory, vol. IT-45, pp. 1435–1455, 1999CrossRefGoogle Scholar
Chang, S. C. and Wolf, J. K., A Simple Derivation of the MacWilliams Identity for Linear Codes, IEEE Transactions on Information Theory, vol. IT-26, pp. 476–477, 1980CrossRefGoogle Scholar
P. Charpin, Open Problems on Cyclic Codes, Handbook of Coding Theory, pp. 963–1063, V. S. Pless and W. C. Huffman, editors, Elsevier, Amsterdam, 1998
Chen, C. L., Computer Results on the Minimum Distance of Some Binary Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-16, pp. 359–360, 1970CrossRefGoogle Scholar
Chevillat, P. R. and Costello, D. J. Jr, An Analysis of Sequential Decoding for Specific Time-Invariant Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-24, pp. 443–451, 1978CrossRefGoogle Scholar
Chien, R. T., Cyclic Decoding Procedures for Bose–Chaudhuri–Hocquenghem Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 357–363, 1964CrossRefGoogle Scholar
Chien, R. T., Burst-Correcting Code with High-Speed Decoding, IEEE Transactions on Information Theory, vol. IT-15, pp. 109–113, 1969CrossRefGoogle Scholar
Chien, R. T., A New Proof of the BCH Bound, IEEE Transactions on Information Theory, vol. IT-18, p. 541, 1972CrossRefGoogle Scholar
Chien, R. T. and Choy, D. M., Algebraic Generalization of BCH–Goppa–Helgert Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 70–79, 1975CrossRefGoogle Scholar
Chien, R. T. and Ng, S. W., Dual Product Codes for Correction of Multiple Low-Density Burst Errors, IEEE Transactions on Information Theory, vol. IT-19, pp. 672–678, 1973CrossRefGoogle Scholar
T. K. Citron, Algorithms and Architectures for Error-Correcting Codes, Ph.D. Dissertation, Stanford University, Stanford, CA, 1986
Cocke, J., Lossless Symbol Coding with Nonprimes, IRE Transactions on Information Theory, vol. IT-5, pp. 33–34, 1959CrossRefGoogle Scholar
Costello, D. J. Jr, A Construction Technique for Random-Error-Correcting Codes, IEEE Transactions on Information Theory, vol. IT-15, pp. 631–636, 1969CrossRefGoogle Scholar
Costello, D. J. Jr, Free Distance Bounds for Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-20, pp. 356–365, 1974CrossRefGoogle Scholar
Delsarte, P., On Subfield Subcodes of Modified Reed–Solomon Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 575–576, 1975CrossRefGoogle Scholar
Delsarte, P., Goethals, J. M., and MacWilliams, F. J., On Generalized Reed–Muller Codes and Their Relatives, Information and Control, vol. 16, pp. 402–442, 1970CrossRefGoogle Scholar
I. Dumer, Recursive Decoding of Reed–Muller Codes, Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing, pp. 61–69, University of Illinois, Monticello, IL, 1999
Elias, P., Error-Free Coding, IRE Transactions on Information Theory, vol. IT-4, pp. 29–37, 1954Google Scholar
Elspas, B., A Note onP-nary Adjacent-Error-Correcting Binary Codes, IRE Transactions on Information Theory, vol. IT-6, pp. 13–15, 1960CrossRefGoogle Scholar
Fano, R. M., A Heuristic Discussion of Probabilistic Decoding, IEEE Transactions on Information Theory, vol. IT-9, pp. 64–74, 1963CrossRefGoogle Scholar
Feng, G. L., A VLSI Architecture for Fast Inversion inGF (2m), IEEE Transactions on Computers, vol. 38, pp. 1383–1386, 1989CrossRefGoogle Scholar
P. Fire, A Class of Multiple-Error Correcting Binary Codes for Non-Independent Errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance Systems Lab., Mountain View, CA, 1959
Forney, G. D. Jr, On Decoding BCH Codes, IEEE Transactions on Information Theory, vol. IT-11, pp. 549–557, 1965CrossRefGoogle Scholar
G. D. Forney, Jr., Concatenated Codes, MIT Press, Cambridge, MA, 1966
G. D. Forney, Jr., Final Report on a Coding System Design for Advanced Solar Mission, Contract NASA-3637, NASA Ames Research Center, Moffet Field, CA, 1967
Forney, G. D. Jr, Convolutional Codes I: Algebraic Structure, IEEE Transactions on Information Theory, vol. IT-16, pp. 720–738, 1970CrossRefGoogle Scholar
Forney, G. D. Jr, Burst-Correcting Codes for the Classic Bursty Channel, IEEE Transactions on Communication Technology, vol. COM-19, pp. 772–781, 1971CrossRefGoogle Scholar
Forney, G. D. Jr, The Viterbi Algorithm, Proceedings of the IEEE, vol. 61, pp. 268–276, 1973CrossRefGoogle Scholar
Forney, G. D. Jr, Minimal Bases of Rational Vector Spaces with Applications to Multiple Variable Linear Systems, SIAM Journal of Control, vol. 13, pp. 493–502, 1973CrossRefGoogle Scholar
Forney, G. D. Jr, Structural Analysis of Convolutional Codes via Dual Codes, IEEE Transactions on Information Theory, vol. IT-19, pp. 512–518, 1973CrossRefGoogle Scholar
Forney, G. D. Jr, Convolutional Codes II: Maximum-Likelihood Decoding and Convolutional Codes III: Sequential Decoding, Information and Control, vol. 25, pp. 222–297, 1974CrossRefGoogle Scholar
G. D. Forney, Jr., The Forward–Backward Algorithm, Proceedings of the Thirty-Fourth Annual Allerton Conference on Communication, Control, and Computing, pp. 432–446, University of Illinois, Monticello, IL, 1996
G. D. Forney, Jr., On Iterative Decoding and the Two-Way Algorithm, Proceedings of the International Symposium on Turbo Codes and Related Topics, Brest, France, 1997
J. B. Fraleigh, A First Course in Abstract Algebra, Second Edition, Addison-Wesley, Reading, MA, 1976
Gallager, R. G., Low-Density Parity-Check Codes, IRE Transactions on Information Theory, vol. IT-8, pp. 21–28, 1962CrossRefGoogle Scholar
R. G. Gallager, Low-Density Parity-Check Codes, The MIT Press, Cambridge, MA, 1963
R. G. Gallager, Information Theory and Reliable Communications, Wiley, New York, NY, 1968
F. R. Gantmacher, The Theory of Matrices, Volume 1 (Second Edition), Chelsea, New York, 1959
Gilbert, E. N., A Comparison of Signaling Alphabets, Bell System Technical Journal, vol. 31, pp. 504–522, 1952CrossRefGoogle Scholar
J. M. Goethals, Threshold Decoding – A Tentative Survey, in Coding and Complexity, G. Longo, editor, Springer-Verlag, New York, NY, 1975
Goethals, J. M. and Delsarte, P., On a Class of Majority-Logic Decodable Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 182–189, 1968CrossRefGoogle Scholar
Golay, M. J. E., Notes on Digital Coding, Proceedings of the IRE, vol. 37, p. 657, 1949Google Scholar
Golay, M. J. E., Notes on the Penny-Weighing Problem, Lossless Symbol Coding with Nonprimes, etc., IRE Transactions on Information Theory, vol. IT-4, pp. 103–109, 1958CrossRefGoogle Scholar
Goppa, V. C., A New Class of Linear Error-Correcting Codes, Problemy Peredachi Informatsii, vol. 6, pp. 24–30, 1970Google Scholar
W. C. Gore, Transmitting Binary Symbols with Reed–Solomon Codes, Proceedings of the Princeton Conference on Information Science Systems, pp. 495–497, Princeton, NJ, 1973
Gorenstein, D. C. and Zierler, N., A Class of Error-Correcting Codes inpmSymbols, Journal of the Society of Industrial and Applied Mathematics, vol. 9, pp. 207–214, 1961CrossRefGoogle Scholar
Green, M. W., Two Heuristic Techniques for Block Code Construction, IEEE Transactions on Information Theory, vol. IT-12, p. 273, 1966Google Scholar
Haccoun, D. and Ferguson, M. J., Generalized Stack Algorithms for Decoding Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 638–651, 1975CrossRefGoogle Scholar
Hagelbarger, D. W., Recurrent Codes: Easily Mechanized Burst Correcting Binary Codes, Bell System Technical Journal, vol. 38, pp. 969–984, 1959CrossRefGoogle Scholar
J. Hagenauer and P. Hoeher, A Viterbi Algorithm with Soft-Decision Outputs and Its Applications, Proceedings of the IEEE GLOBECOM' 89, pp. 47.1.1–47.1.7, 1989
Hamming, R. W., Error Detecting and Error Correcting Codes, Bell System Technical Journal, vol. 29, pp. 147–160, 1950CrossRefGoogle Scholar
Hartmann, C. R. P., Decoding Beyond the BCH Bound, IEEE Transactions on Information Theory, vol. IT-18, pp. 441–444, 1972CrossRefGoogle Scholar
J. A. Heller, Short Constraint Length Convolutional Codes, Jet Propulsion Laboratory Space Program Summary, 37–54 III, pp. 171–177, 1968
Hocquenghem, A., Codes Correcteurs D'erreurs, Chiffres, vol. 2, pp. 147–156, 1959Google Scholar
Huber, K., Some Comments on Zech's Logarithms, IEEE Transactions on Information Theory, vol. IT-36, pp. 946–950, 1990CrossRefGoogle Scholar
Huntoon, Z. McC. and Michelson, A. M., On the Computation of the Probability of Post-Decoding Error Events for Block Codes, IEEE Transactions on Information Theory, vol. IT-23, pp. 399–403, 1977CrossRefGoogle Scholar
K. Imamura, Self-Complementary Bases of Finite Fields, Book of Abstracts – 1983 IEEE International Symposium on Information Theory, St. Jovite, Canada, 1983
K. Imamura, W. Yoshida, and N. Nakamura, Some Notes on the Binary Weight Distribution of Reed–Solomon Codes, Book of Abstracts – 1986 IEEE International Symposium on Information Theory, Ann Arbor, MI, 1986
Jacobs, I. M. and Berlekamp, E. R., A Lower Bound to the Distribution of Computations for Sequential Decoding, IEEE Transactions on Information Theory, vol. IT-13, pp. 167–174, 1967CrossRefGoogle Scholar
F. Jelinek, Probabilistic Information Theory, McGraw-Hill, New York, 1968
Jelinek, F., An Upper Bound on Moments of Sequential Decoding Effort, IEEE Transactions on Information Theory, vol. IT-15, pp. 140–149, 1969CrossRefGoogle Scholar
J. M. Jensen, On Decoding Doubly Extended Reed–Solomon Codes, Proceedings – 1995 IEEE International Symposium on Information, Whistler, BC, Canada, 1995
Johannesson, R., Robustly Optimal Rate One-Half Binary Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 464–468, 1975CrossRefGoogle Scholar
R. Johannesson and K. Sh. Zigangirov, Fundamentals of Convolutional Coding, IEEE Press, Piscataway, NJ, 1999
Justesen, J., A Class of Constructive Asymptotically Good Algebraic Codes, IEEE Transactions on Information Theory, vol. IT-18, pp. 652–656, 1972CrossRefGoogle Scholar
Kasahara, M., Sugiyama, Y., Hirasawa, S., and Namekawa, T., A New Class of Binary Codes Constructed on the Basis of BCH Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 582–585, 1975CrossRefGoogle Scholar
Kasami, T., Systematic Codes Using Binary Shift Register Sequences, Journal of the Information Processing Society of Japan, vol. 1, pp. 198–200, 1960Google Scholar
Kasami, T., Optimum Shortened Cyclic Codes for Burst-Error Correction, IEEE Transactions on Information Theory, vol. IT-9, pp. 105–109, 1963CrossRefGoogle Scholar
Kasami, T., A Decoding Procedure for Multiple-Error-Correcting Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 134–139, 1964CrossRefGoogle Scholar
Kasami, T. and Lin, S., The Binary Weight Distribution of the Extended (2m, 2m −4) Code of the Reed–Solomon Code overGF(2m) with Generator Polynomial (x−α)(x−α2)(x−α3), Linear Algebra and Its Applications, vol. 98, pp. 291–307, 1988CrossRefGoogle Scholar
Kasami, T. and Tokura, N., Some Remarks on BCH Bounds and Minimum Weights of Binary Primitive BCH Codes, IEEE Transactions on Information Theory, vol. IT-15, pp. 408–412, 1969CrossRefGoogle Scholar
T. Kasami, S. Lin, and W. W. Peterson, Some Results on Cyclic Codes Which are Invariant Under the Affine Group, Air Force Cambridge Research Labs Report, Cambridge, MA, 1966
Kasami, T., Lin, S., and Peterson, W. W., Some Results on Weight Distributions of BCH Codes, IEEE Transactions on Information Theory, vol. IT-12, p. 274, 1966Google Scholar
Kasami, T., Lin, S., and Peterson, W. W., New Generalizations of the Reed–Muller Codes – Part I: Primitive Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 189–199, 1968CrossRefGoogle Scholar
Kasami, T., Lin, S., and Peterson, W. W., Polynomial Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 807–814, 1968CrossRefGoogle Scholar
Z. Kiyasu, Research and Development Data No. 4, Electrical Communications Laboratory, Nippon Telegraph Corporation, Tokyo, Japan, 1953
Kolesnik, V. D. and Mironchikov, E. T., Some Cyclic Codes and a Scheme for Decoding by a Majority of Tests, Problemy Peredachi Informatsii, vol. 1, pp. 1–12, 1965Google Scholar
Kolesnik, V. D. and Mironchikov, E. T., Cyclic Reed–Muller Codes and Their Decoding, Problemy Peredachi Informatsii, vol. 4, pp. 15–19, 1968Google Scholar
Larsen, K. J., Short Convolutional Codes with Maximal Free Distance for Rate 1/2, 1/3, and 1/4, IEEE Transactions on Information Theory, vol. IT-19, pp. 371–372, 1973CrossRefGoogle Scholar
Laws, B. A. Jr and Rushforth, C. K., A Cellular-Array Multiplier forGF(2m), IEEE Transactions on Computers, vol. C-20, pp. 1573–1578, 1971CrossRefGoogle Scholar
Lee, P. J., There are Many Good Periodically Time-Varying Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-35, pp. 460–463, 1989CrossRefGoogle Scholar
Lempel, A., Characterization and Synthesis of Self-Complementary Normal Bases in Finite Fields, Linear Algebra and Its Applications, vol. 98, pp. 331–346, 1988CrossRefGoogle Scholar
Lempel, A. and Winograd, S., A New Approach to Error-Correcting Codes, IEEE Transactions on Information Theory, vol. IT-23, pp. 503–508, 1977CrossRefGoogle Scholar
Lidl, R. and Niederreiter, H., Finite Fields: Encyclopedia of Mathematics and its Applications, vol. 20, Cambridge University Press, Cambridge, UK, 1984
Lin, S. and Markowsky, G., On a Class of One-Step Majority-Logic Decodable Cyclic Codes, IBM Journal of Research and Development, vol. 24, pp. 56–63, 1980CrossRefGoogle Scholar
Ma, J. H. and Wolf, J. K., On Tail-Biting Convolutional Codes, IEEE Transactions on Communications, vol. COM-34, pp. 1049–1053, 1988Google Scholar
MacWilliams, F. J., A Theorem on the Distribution of Weights in a Systematic Code, Bell System Technical Journal, vol. 42, pp. 79–94, 1963CrossRefGoogle Scholar
MacWilliams, F. J., Permutation Decoding of Systematic Codes, Bell System Technical Journal, vol. 43, pp. 485–505, 1964CrossRefGoogle Scholar
Mandelbaum, D. M., On Decoding of Reed–Solomon Codes, IEEE Transactions on Information Theory, vol. IT-17, pp. 707–712, 1971CrossRefGoogle Scholar
Mandelbaum, D. M., Decoding Beyond the Designed Distance for Certain Algebraic Codes, Information and Control, vol. 35, pp. 209–228, 1977CrossRefGoogle Scholar
Mandelbaum, D. M., Construction of Error-Correcting Codes by Interpolation, IEEE Transactions on Information Theory, vol. IT-25, pp. 27–35, 1979CrossRefGoogle Scholar
Mann, H. B., On the Number of Information Symbols in Bose–Chaudhuri Codes, Information and Control, vol. 5, pp. 153–162, 1962CrossRefGoogle Scholar
J. L. Massey, Threshold Decoding, MIT Press, Cambridge, MA, 1963
Massey, J. L., Shift-Register Synthesis and BCH Decoding, IEEE Transactions on Information Theory, vol. IT-15, pp. 122–127, 1969CrossRefGoogle Scholar
J. L. Massey, Error bounds for tree codes, trellis codes and convolutional codes with encoding and decoding procedures, in Coding and Complexity, G. Longo, editor, Springer-Verlag, New York, NY, 1975
J. L. Massey, Coding theory, Chapter 16 of Handbook of Applicable Mathematics, Volume V, Part B of Combinatorics and Geometry, W. Ledermann and S. Vajda, editors, Wiley, Chichester and New York, NY, 1985
Massey, J. L. and Sain, M. K., Inverses of Linear Sequential Circuits, IEEE Transactions on Computers, vol. C-17, pp. 330–337, 1968CrossRefGoogle Scholar
Mattson, H. F. and Solomon, G., A New Treatment of Bose–Chaudhuri Codes, Journal of the Society of Industrial and Applied Mathematics, vol. 9, pp. 654–669, 1961CrossRefGoogle Scholar
U. Maurer and R. Viscardi, Running-Key Generators with Memory in the Nonlinear Combining Function, Diploma Thesis, Swiss Federal Institute of Technology, Zurich, 1984
R. J. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer, Boston, MA, 1987
R. J. McEliece, The algebraic theory of convolutional codes, in Handbook of Coding Theory, pp. 1065–1138, V. S. Pless and W. C. Huffman, editors, Elsevier, Amsterdam, 1998
McEliece, R. J., MacKay, D. J. C., and Cheng, J. F., Turbo Decoding as an Instance of Pearl's ‘Belief Propagation’ Algorithm, IEEE Journal on Selected Areas in Communication, vol. SAC-16, pp. 140–152, 1998CrossRefGoogle Scholar
McEliece, R. J. and Onyszchuk, I., The Analysis of Convolutional Codes via the Extended Smith Algorithm, Jet Propulsion Laboratory TDA Progress Report, vol. 42–112, pp. 22–30, 1993Google Scholar
McEliece, R. J., Rodemich, E. R., Rumsey, H. Jr, and Welch, L. R., New Upper Bounds on the Rate of a Code Via the Delsarte–MacWilliams Inequalities, IEEE Transactions on Information Theory, vol. IT-23, pp. 157–166, 1977CrossRefGoogle Scholar
Meggitt, J. E., Error-Correcting Codes for Correcting Bursts of Errors, IBM Journal of Research and Development, vol. 4, pp. 329–334, 1960CrossRefGoogle Scholar
Meggitt, J. E., Error-Correcting Codes and Their Implementation, IRE Transactions on Information Theory, vol. IT-7, pp. 232–244, 1961Google Scholar
A. Michelson, A Fast Transform in Some Galois Fields and an Application to Decoding Reed-Solomon Codes, IEEE Abstracts of Papers – IEEE International Symposium on Information Theory, Ronneby, Sweden, 1976
M. E. Mitchell, Error-Trap Decoding of Cyclic Codes, G.E. Report No. 62MCD3, General Electric Military Communications Department, Oklahoma City, OK, 1962
Morii, M., Kasahara, M., and Whiting, D. L., Efficient Bit-Serial Multiplication and the Discrete-Time Wiener–Hopf Equation over Finite Fields, IEEE Transactions on Information Theory, vol. IT-35, pp. 1177–1183, 1989CrossRefGoogle Scholar
Muder, D. J., Minimal Trellises for Block Codes, IEEE Transactions on Information Theory, vol. IT-34, pp. 1049–1053, 1988CrossRefGoogle Scholar
Muller, D. E., Application of Boolean Algebra to Switching Circuit Design and to Error Detection, IRE Transactions on Electronic Computers, vol. EC-3, pp. 6–12, 1954Google Scholar
J. P. Odenwalder, Optimal Decoding of Convolutional Codes, Ph.D. Dissertation, University of California at Los Angeles, Los Angeles, CA, 1970
J. K. Omura and J. L. Massey, Computational Method and Apparatus for Finite Field Arithmetic, U.S. Patent 4 587 627, May 6, 1986 (Filed September 14, 1982)
Paaske, E., Short Binary Convolutional Codes with Maximal Free Distance for Rates 2/3, and 3/4, IEEE Transactions on Information Theory, vol. IT-20, pp. 683–689, 1974CrossRefGoogle Scholar
R. H. Paschburg, Software Implementation of Error-Correcting Codes, M.S. Thesis, University of Illinois, Urbana, IL, 1974
Peterson, W. W., Encoding and Error-Correction Procedures for the Bose–Chaudhuri Codes, IRE Transactions on Information Theory, vol. IT-6, pp. 459–470, 1960CrossRefGoogle Scholar
W. W. Peterson, Error Correcting Codes, MIT Press, Cambridge, MA, and Wiley, New York, NY, 1961
W. W. Peterson and E. J. Weldon, Jr., Error Correcting Codes, Second Edition, MIT Press, Cambridge, MA, 1972
Pless, V., Power Moment Identities on Weight Distributions in Error Correcting Codes, Information and Control, vol. 6, pp. 147–152, 1963CrossRefGoogle Scholar
Pless, V. S., On the Uniqueness of the Golay Codes, Journal of Combinatoric Theory, vol. 5, pp. 215–228, 1968CrossRefGoogle Scholar
Plotkin, M., Binary Codes with Specified Minimum Distances, IEEE Transactions on Information Theory, vol. IT-6, pp. 445–450, 1960CrossRefGoogle Scholar
Pollard, J. M., The Fast Fourier Transform in a Finite Field, Mathematics of Computation, vol. 25, pp. 365–374, 1971CrossRefGoogle Scholar
E. Prange, Cyclic Error-Correcting Codes in Two Symbols, AFCRC-TN-57–103, Air Force Cambridge Research Center, Cambridge, MA, 1957
E. Prange, Some Cyclic Error-Correcting Codes with Simple Decoding Algorithms, AFCRC-TN-58–156, Air Force Cambridge Research Center, Bedford, MA, 1958
Reed, I. S., A Class of Multiple-Error-Correcting Codes and the Decoding Scheme, IRE Transactions on Information Theory, vol. IT-4, pp. 38–49, 1954Google Scholar
Reed, I. S. and Solomon, G., Polynomial Codes over Certain Finite Fields, Journal of the Society of Industrial and Applied Mathematics, vol. 8, pp. 300–304, 1960CrossRefGoogle Scholar
Retter, C. T., The Average Binary Weight-Enumerator for a Class of Generalized Reed–Solomon Codes, IEEE Transactions on Information Theory, vol. IT-37, pp. 346–349, 1991CrossRefGoogle Scholar
Robinson, J. P. and Bernstein, A. J., A Class of Recurrent Codes with Limited Error Propagation, IEEE Transactions on Information Theory, vol. IT-13, pp. 106–113, 1967CrossRefGoogle Scholar
L. D. Rudolph, Geometric Configuration and Majority-Logic Decodable Codes, M.E.E. Thesis, University of Oklahoma, Norman, OK, 1964
Rudolph, L. D., A Class of Majority-Logic Decodable Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 305–307, 1967CrossRefGoogle Scholar
Rudolph, L. and Mitchell, M. E., Implementation of Decoders for Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 259–260, 1964CrossRefGoogle Scholar
Sarwate, D. V. and Morrison, R. D., Decoder Malfunction in BCH Decoders, IEEE Transactions on Information Theory, vol. IT-36, pp. 884–889, 1990CrossRefGoogle Scholar
Sarwate, D. V. and Shanbhag, N. R., High-Speed Architecture for Reed–Solomon Decoders, IEEE Transactions on VLSI Systems, vol. VLSI-9, pp. 641–655, 2001CrossRefGoogle Scholar
Savage, J. E., Minimum Distance Estimates of the Performance of Sequential Decoding, IEEE Transactions on Information Theory, vol. IT-15, pp. 128–140, 1969CrossRefGoogle Scholar
T. Schaub, A Linear Complexity Approach to Cyclic Codes, Doctor of Technical Sciences Dissertation, Swiss Federal Institute of Technology, Zurich, 1988
Schönheim, J., On Linear and Nonlinear Single-Error-Correctingq-nary Perfect Codes, Information and Control, vol. 12, pp. 23–26, 1968CrossRefGoogle Scholar
C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol. 27, pp. 379–423, 1948 (Part I), pp. 623–656 (Part II) reprinted in book form with postscript by W. Weaver, University of Illinois Press, Urbana, IL, 1949; Anniversary Edition, 1998
Shao, H. M., Truong, T. K., Deutsch, L. J., Yuen, J. H., and Reed, I. S., A VLSI Design of a Pipeline Reed–Solomon Decoder, IEEE Transactions on Computers, vol. C-34, pp. 393–403, 1985CrossRefGoogle ScholarPubMed
Singleton, R. C., Maximum Distanceq-nary Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 116–118, 1964CrossRefGoogle Scholar
Slepian, D., A Class of Binary Signaling Alphabets, Bell System Technical Journal, vol. 35, pp. 203–234, 1956CrossRefGoogle Scholar
Slepian, D., Some Further Study of Group Codes, Bell System Technical Journal, vol. 39, pp. 1219–1252, 1960CrossRefGoogle Scholar
Sloane, N. J. A., Reddy, S. M., and Chen, C. L., New Binary Codes, IEEE Transactions on Information Theory, vol. IT-18, pp. 503–510, 1972CrossRefGoogle Scholar
Smith, H. J. S., On Systems of Linear Indeterminant Equations and Congruences, Philosophical Transactions of the Royal Society, vol. 151, pp. 293–326, 1861CrossRefGoogle Scholar
Solomon, G. and Tilborg, H. C. A., A Connection Between Block and Convolutional Codes, SIAM Journal of Applied Mathematics, vol. 37, pp. 358–369, 1979CrossRefGoogle Scholar
G. Strang, Linear Algebra and Its Applications, Second Edition, Academic Press, New York, NY, 1980
Sudan, M., Decoding of Reed–Solomon Codes Beyond the Error-Correction Bound, Journal of Complexity, vol. 13, pp. 180–183, 1997CrossRefGoogle Scholar
M. Sudan, Decoding of Reed–Solomon Codes Beyond the Error-Correction Diameter, Proceedings of the Thirty-Fifth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, IL, 1997
Sugiyama, Y., Kasahara, M., Hirasawa, S., and Namekawa, T., A Method for Solving Key Equation for Decoding Goppa Codes, Information and Control, vol. 27, pp. 87–99, 1975CrossRefGoogle Scholar
Tanner, R. M., A Recursive Approach to Low-Complexity Codes, IEEE Transactions on Information Theory, vol. IT-27, pp. 535–547, 1981Google Scholar
R. M. Thrall and L. Tornheim, Vector Spaces and Matrices, Wiley, New York, NY, 1957
A. Tietäväinen, A Short Proof for the Nonexistence of Unknown Perfect Codes over GF(q), q《2, Annales Acad. Scient. Fennicae, Ser. A., no. 580, pp. 1–6, 1974
Tsfasman, M. A., Vladut, S. G., and Zink, Th., Modular Curves, Shimura Curves, and Goppa Codes Better Than the Varshamov–Gilbert Bound, Math. Nachr., vol. 104, pp. 13–28, 1982Google Scholar
Ungerboeck, G., Channel Coding with Multilevel Phase Signals, IEEE Transactions on Information Theory, vol. IT-28, pp. 55–67, 1982CrossRefGoogle Scholar
B. L. Van der Waerden, Modern Algebra (two volumes), translated by F. Blum and T. J. Benac, Frederick Ungar, New York, NY, 1950 and 1953
Lint, J. H., A Survey of Perfect Codes, Rocky Mountain Journal of Mathematics, vol. 5, pp. 199–224, 1975CrossRefGoogle Scholar
Vanderhorst, J. and Berger, T., Complete Decoding of Triple-Error-Correcting Binary BCH Codes, IEEE Transactions on Information Theory, vol. IT-22, pp. 138–147, 1976CrossRefGoogle Scholar
A. Vardy, Trellis Structure of Codes, in Handbook of Coding Theory, editors, V. S. Pless and W. C. Huffman, Elsevier Science, Amsterdam, 1999
Varshamov, R. R., Estimate of the Number of Signals in Error Correcting Codes, Doklady Akad. Nauk SSSR, vol. 117, pp. 739–741, 1957Google Scholar
Vasilýev, Y. L., On Nongroup Close-Packed Codes, Problemi Cybernetica, vol. 8, pp. 337–339, 1962Google Scholar
Viterbi, A. J., Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm, IEEE Transactions on Information Theory, vol. IT-13, pp. 260–269, 1967CrossRefGoogle Scholar
A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding, McGraw-Hill, 1979
L. R. Welch and E. R. Berlekamp, Error Correction for Algebraic Block Codes, US Patent 4 633 470, 1983
Welch, L. R. and Scholtz, R. A., Continued Fractions and Berlekamp's Algorithm, IEEE Transactions on Information Theory, vol. IT-25, pp. 19–27, 1979CrossRefGoogle Scholar
E. J. Weldon, Jr., euclidean Geometry Cyclic Codes, Proceedings of the Symposium on Combinatorial Mathematics, University of North Carolina, Chapel Hill, NC, 1967
Weldon, E. J. Jr, New Generalizations of the Reed–Muller Codes – Part II: Non-Primitive Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 199–206, 1968CrossRefGoogle Scholar
N. Wiberg, Codes Depending on General Graphs, Doctor of Philosophy Dissertation, Department of Electrical Engineering, University of Linkoping, Sweden, 1996
Wiberg, N., Loeliger, H. A., and Kötter, R., Codes and Iterative Decoding on General Graphs, European Transactions on Telecommunications, vol. 6, pp. 513–526, 1995CrossRefGoogle Scholar
Willett, M., Arithmetic in a Finite Field, Mathematics of Computation, vol. 35, pp. 1353–1359, 1980CrossRefGoogle Scholar
Wolf, J. K., Adding Two Information Symbols to Certain Nonbinary BCH Codes and Some Applications, Bell System Technical Journal, vol. 48, pp. 2405–2424, 1969CrossRefGoogle Scholar
Wolf, J. K., Efficient Maximum-Likelihood Decoding of Linear Block Codes Using a Trellis, IEEE Transactions on Information Theory, vol. 24, pp. 76–80, 1978CrossRefGoogle Scholar
Wozencraft, J. M., Sequential Decoding for Reliable Communication, 1957 National IRE Convention Record, vol. 5, Part 2, pp. 11–25, 1957Google Scholar
J. M. Wozencraft and B. Reiffen, Sequential Decoding, MIT Press, Cambridge, MA, 1961
W. W. Wu, New Convolutional Codes, IEEE Transactions on Communication Theory, Part I, vol. COM-23, pp. 942–956, 1975; Part II, vol. COM-24, pp. 19–33, 1976; Part III, vol. COM-24, pp. 946–955, 1976
Wyner, A. D. and Ash, R. B., Analysis of Recurrent Codes, IEEE Transactions on Information Theory, vol. IT-9, pp. 143–156, 1963CrossRefGoogle Scholar
N. Zierler, On a Variation of the First Order Reed–Muller Codes, Massachusetts Institute of Technology Lincoln Laboratory Group Report 34–80, Lexington, MA, 1958
Zigangirov, K., Sequential Decoding Procedures, Problemy Peredachi Informatsii, vol. 2, pp. 13–25, 1966.Google Scholar
Abramson, N. A., Class of Systematic Codes for Non-Independent Errors, IRE Transactions on Information Theory, vol. IT-5, pp. 150–157, 1959CrossRefGoogle Scholar
Abramson, N. A., A Note on Single Error-Correcting Binary Codes, IRE Transactions on Information Theory, vol. IT-6, pp. 502–503, 1960CrossRefGoogle Scholar
V. I. Andryanov and V. N. Saskovets, Decoding Codes, Akad. Nauk. Ukr. SSR Kibernetika, Part 1, 1966
Arimoto, S., Encoding and Decoding of p-ary Group Codes and the Correction System (in Japanese), Information Processing in Japan, vol. 2, pp. 321–325, 1961Google Scholar
Assmus, E. F. Jr and Mattson, H. F. Jr, Coding and Combinatorics, SIAM Review, vol. 16, pp. 349–388, 1974CrossRefGoogle Scholar
E. F. Assmus, Jr., H. F. Mattson, Jr., and R. J. Turyn, Cyclic Codes, AFCRL-65–332, Air Force Cambridge Research Labs, Bedford, MA, 1965
Baggen, C. P. M. J. and Tolhuizen, L. M. G. M., On Diamond Codes, IEEE Transactions on Information Theory, vol. IT-43, pp. 1400–1411, 1997CrossRefGoogle Scholar
Bahl, L. R. and Jelinek, F., Rate 1/2 Convolutional Codes with Complementary Generators, IEEE Transactions on Information Theory, vol. IT-17, pp. 718–727, 1971CrossRefGoogle Scholar
Bahl, L. R., Cocke, J., Jelinek, F., and Raviv, J., Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate, IEEE Transactions on Information Theory, vol. IT-20, pp. 284–287, 1974CrossRefGoogle Scholar
Bartee, T. C. and Schneider, D. I., Computation with Finite Fields, Information and Control, vol. 6, pp. 79–98, 1963CrossRefGoogle Scholar
Bassalygo, L. A., New Upper Bounds for Error Correcting Codes, Problemy Peredachi Informatsii, vol. 1, pp. 41–45, 1965Google Scholar
B. Baumslag and B. Chandler, Theory and Problems of Group Theory, Schaum's Outline Series, McGraw-Hill, New York, NY, 1968
Berlekamp, E. R., The Enumeration of Information Symbols in BCH Codes, Bell System Technical Journal, vol. 46, pp. 1861–1880, 1967CrossRefGoogle Scholar
E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, NY, 1968
Berlekamp, E. R., Long Primitive Binary BCH Codes Have Distanced ∼ 2n ln R−1log n …, IEEE Transactions on Information Theory, vol. IT-18, pp. 415–416, 1972CrossRefGoogle Scholar
Berlekamp, E. R., Bit Serial Reed–Solomon Encoders, IEEE Transactions on Information Theory, vol. IT-28, pp. 869–874, 1982CrossRefGoogle Scholar
Berrou, C. and Glavieux, A., Near Optimum Error Correcting Coding and Decoding: Turbo-Codes, IEEE Transactions on Communications, vol. COM-44, pp. 1261–1271, 1996CrossRefGoogle Scholar
C. Berrou, A. Glavieux, and P. Thitimajshima, Near Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes, Proceedings of the IEEE International Conference on Communications, Geneva, Switzerland, IEEE, Piscataway, NJ, 1993
G. Birkhoff and S. MacLane, A Survey of Modern Algebra, Revised Edition, Macmillan, New York, NY, 1953
R. E. Blahut, Algebraic decoding in the frequency domain, in Algebraic Coding Theory and Practice, G. Longo, editor, Springer-Verlag, New York, NY, 1979
Blahut, R. E., Transform Techniques for Error-Control Codes, IBM Journal of Research and Development, vol. 23, pp. 299–315, 1979CrossRefGoogle Scholar
R. E. Blahut, On Extended BCH Codes, Proceedings of the Eighteenth Annual Allerton Conference on Communication, Control, and Computers, pp. 50–59, University of Illinois, Monticello, IL, 1980
Blahut, R. E., A Universal Reed–Solomon Decoder, IBM Journal of Research and Development, vol. 28, pp. 150–158, 1984CrossRefGoogle Scholar
R. A. Blum and A. D. Weiss, Further Results in Error-Correcting Codes, S.M. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1960
Bose, R. C. and Ray-Chaudhuri, D. K., On a Class of Error-Correcting Binary Group Codes, Information and Control, vol. 3, pp. 68–79, 1960CrossRefGoogle Scholar
Burton, H. O., Inversionless Decoding of Binary BCH Codes, IEEE Transactions on Information Theory, vol. IT-17, pp. 464–466, 1971CrossRefGoogle Scholar
Burton, H. O. and Weldon, E. J. Jr, Cyclic Product Codes, IEEE Transactions on Information Theory, vol. IT-11, pp. 433–439, 1965CrossRefGoogle Scholar
Bussgang, J. J., Some Properties of Binary Convolutional Code Generators, IEEE Transactions on Information Theory, vol. IT-11, pp. 90–100, 1965CrossRefGoogle Scholar
Calderbank, A. R., Forney, G. D. Jr, and Vardy, A., Minimal Tail-Biting Trellis: The Golay Code and More, IEEE Transactions on Information Theory, vol. IT-45, pp. 1435–1455, 1999CrossRefGoogle Scholar
Chang, S. C. and Wolf, J. K., A Simple Derivation of the MacWilliams Identity for Linear Codes, IEEE Transactions on Information Theory, vol. IT-26, pp. 476–477, 1980CrossRefGoogle Scholar
P. Charpin, Open Problems on Cyclic Codes, Handbook of Coding Theory, pp. 963–1063, V. S. Pless and W. C. Huffman, editors, Elsevier, Amsterdam, 1998
Chen, C. L., Computer Results on the Minimum Distance of Some Binary Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-16, pp. 359–360, 1970CrossRefGoogle Scholar
Chevillat, P. R. and Costello, D. J. Jr, An Analysis of Sequential Decoding for Specific Time-Invariant Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-24, pp. 443–451, 1978CrossRefGoogle Scholar
Chien, R. T., Cyclic Decoding Procedures for Bose–Chaudhuri–Hocquenghem Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 357–363, 1964CrossRefGoogle Scholar
Chien, R. T., Burst-Correcting Code with High-Speed Decoding, IEEE Transactions on Information Theory, vol. IT-15, pp. 109–113, 1969CrossRefGoogle Scholar
Chien, R. T., A New Proof of the BCH Bound, IEEE Transactions on Information Theory, vol. IT-18, p. 541, 1972CrossRefGoogle Scholar
Chien, R. T. and Choy, D. M., Algebraic Generalization of BCH–Goppa–Helgert Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 70–79, 1975CrossRefGoogle Scholar
Chien, R. T. and Ng, S. W., Dual Product Codes for Correction of Multiple Low-Density Burst Errors, IEEE Transactions on Information Theory, vol. IT-19, pp. 672–678, 1973CrossRefGoogle Scholar
T. K. Citron, Algorithms and Architectures for Error-Correcting Codes, Ph.D. Dissertation, Stanford University, Stanford, CA, 1986
Cocke, J., Lossless Symbol Coding with Nonprimes, IRE Transactions on Information Theory, vol. IT-5, pp. 33–34, 1959CrossRefGoogle Scholar
Costello, D. J. Jr, A Construction Technique for Random-Error-Correcting Codes, IEEE Transactions on Information Theory, vol. IT-15, pp. 631–636, 1969CrossRefGoogle Scholar
Costello, D. J. Jr, Free Distance Bounds for Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-20, pp. 356–365, 1974CrossRefGoogle Scholar
Delsarte, P., On Subfield Subcodes of Modified Reed–Solomon Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 575–576, 1975CrossRefGoogle Scholar
Delsarte, P., Goethals, J. M., and MacWilliams, F. J., On Generalized Reed–Muller Codes and Their Relatives, Information and Control, vol. 16, pp. 402–442, 1970CrossRefGoogle Scholar
I. Dumer, Recursive Decoding of Reed–Muller Codes, Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing, pp. 61–69, University of Illinois, Monticello, IL, 1999
Elias, P., Error-Free Coding, IRE Transactions on Information Theory, vol. IT-4, pp. 29–37, 1954Google Scholar
Elspas, B., A Note onP-nary Adjacent-Error-Correcting Binary Codes, IRE Transactions on Information Theory, vol. IT-6, pp. 13–15, 1960CrossRefGoogle Scholar
Fano, R. M., A Heuristic Discussion of Probabilistic Decoding, IEEE Transactions on Information Theory, vol. IT-9, pp. 64–74, 1963CrossRefGoogle Scholar
Feng, G. L., A VLSI Architecture for Fast Inversion inGF (2m), IEEE Transactions on Computers, vol. 38, pp. 1383–1386, 1989CrossRefGoogle Scholar
P. Fire, A Class of Multiple-Error Correcting Binary Codes for Non-Independent Errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance Systems Lab., Mountain View, CA, 1959
Forney, G. D. Jr, On Decoding BCH Codes, IEEE Transactions on Information Theory, vol. IT-11, pp. 549–557, 1965CrossRefGoogle Scholar
G. D. Forney, Jr., Concatenated Codes, MIT Press, Cambridge, MA, 1966
G. D. Forney, Jr., Final Report on a Coding System Design for Advanced Solar Mission, Contract NASA-3637, NASA Ames Research Center, Moffet Field, CA, 1967
Forney, G. D. Jr, Convolutional Codes I: Algebraic Structure, IEEE Transactions on Information Theory, vol. IT-16, pp. 720–738, 1970CrossRefGoogle Scholar
Forney, G. D. Jr, Burst-Correcting Codes for the Classic Bursty Channel, IEEE Transactions on Communication Technology, vol. COM-19, pp. 772–781, 1971CrossRefGoogle Scholar
Forney, G. D. Jr, The Viterbi Algorithm, Proceedings of the IEEE, vol. 61, pp. 268–276, 1973CrossRefGoogle Scholar
Forney, G. D. Jr, Minimal Bases of Rational Vector Spaces with Applications to Multiple Variable Linear Systems, SIAM Journal of Control, vol. 13, pp. 493–502, 1973CrossRefGoogle Scholar
Forney, G. D. Jr, Structural Analysis of Convolutional Codes via Dual Codes, IEEE Transactions on Information Theory, vol. IT-19, pp. 512–518, 1973CrossRefGoogle Scholar
Forney, G. D. Jr, Convolutional Codes II: Maximum-Likelihood Decoding and Convolutional Codes III: Sequential Decoding, Information and Control, vol. 25, pp. 222–297, 1974CrossRefGoogle Scholar
G. D. Forney, Jr., The Forward–Backward Algorithm, Proceedings of the Thirty-Fourth Annual Allerton Conference on Communication, Control, and Computing, pp. 432–446, University of Illinois, Monticello, IL, 1996
G. D. Forney, Jr., On Iterative Decoding and the Two-Way Algorithm, Proceedings of the International Symposium on Turbo Codes and Related Topics, Brest, France, 1997
J. B. Fraleigh, A First Course in Abstract Algebra, Second Edition, Addison-Wesley, Reading, MA, 1976
Gallager, R. G., Low-Density Parity-Check Codes, IRE Transactions on Information Theory, vol. IT-8, pp. 21–28, 1962CrossRefGoogle Scholar
R. G. Gallager, Low-Density Parity-Check Codes, The MIT Press, Cambridge, MA, 1963
R. G. Gallager, Information Theory and Reliable Communications, Wiley, New York, NY, 1968
F. R. Gantmacher, The Theory of Matrices, Volume 1 (Second Edition), Chelsea, New York, 1959
Gilbert, E. N., A Comparison of Signaling Alphabets, Bell System Technical Journal, vol. 31, pp. 504–522, 1952CrossRefGoogle Scholar
J. M. Goethals, Threshold Decoding – A Tentative Survey, in Coding and Complexity, G. Longo, editor, Springer-Verlag, New York, NY, 1975
Goethals, J. M. and Delsarte, P., On a Class of Majority-Logic Decodable Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 182–189, 1968CrossRefGoogle Scholar
Golay, M. J. E., Notes on Digital Coding, Proceedings of the IRE, vol. 37, p. 657, 1949Google Scholar
Golay, M. J. E., Notes on the Penny-Weighing Problem, Lossless Symbol Coding with Nonprimes, etc., IRE Transactions on Information Theory, vol. IT-4, pp. 103–109, 1958CrossRefGoogle Scholar
Goppa, V. C., A New Class of Linear Error-Correcting Codes, Problemy Peredachi Informatsii, vol. 6, pp. 24–30, 1970Google Scholar
W. C. Gore, Transmitting Binary Symbols with Reed–Solomon Codes, Proceedings of the Princeton Conference on Information Science Systems, pp. 495–497, Princeton, NJ, 1973
Gorenstein, D. C. and Zierler, N., A Class of Error-Correcting Codes inpmSymbols, Journal of the Society of Industrial and Applied Mathematics, vol. 9, pp. 207–214, 1961CrossRefGoogle Scholar
Green, M. W., Two Heuristic Techniques for Block Code Construction, IEEE Transactions on Information Theory, vol. IT-12, p. 273, 1966Google Scholar
Haccoun, D. and Ferguson, M. J., Generalized Stack Algorithms for Decoding Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 638–651, 1975CrossRefGoogle Scholar
Hagelbarger, D. W., Recurrent Codes: Easily Mechanized Burst Correcting Binary Codes, Bell System Technical Journal, vol. 38, pp. 969–984, 1959CrossRefGoogle Scholar
J. Hagenauer and P. Hoeher, A Viterbi Algorithm with Soft-Decision Outputs and Its Applications, Proceedings of the IEEE GLOBECOM' 89, pp. 47.1.1–47.1.7, 1989
Hamming, R. W., Error Detecting and Error Correcting Codes, Bell System Technical Journal, vol. 29, pp. 147–160, 1950CrossRefGoogle Scholar
Hartmann, C. R. P., Decoding Beyond the BCH Bound, IEEE Transactions on Information Theory, vol. IT-18, pp. 441–444, 1972CrossRefGoogle Scholar
J. A. Heller, Short Constraint Length Convolutional Codes, Jet Propulsion Laboratory Space Program Summary, 37–54 III, pp. 171–177, 1968
Hocquenghem, A., Codes Correcteurs D'erreurs, Chiffres, vol. 2, pp. 147–156, 1959Google Scholar
Huber, K., Some Comments on Zech's Logarithms, IEEE Transactions on Information Theory, vol. IT-36, pp. 946–950, 1990CrossRefGoogle Scholar
Huntoon, Z. McC. and Michelson, A. M., On the Computation of the Probability of Post-Decoding Error Events for Block Codes, IEEE Transactions on Information Theory, vol. IT-23, pp. 399–403, 1977CrossRefGoogle Scholar
K. Imamura, Self-Complementary Bases of Finite Fields, Book of Abstracts – 1983 IEEE International Symposium on Information Theory, St. Jovite, Canada, 1983
K. Imamura, W. Yoshida, and N. Nakamura, Some Notes on the Binary Weight Distribution of Reed–Solomon Codes, Book of Abstracts – 1986 IEEE International Symposium on Information Theory, Ann Arbor, MI, 1986
Jacobs, I. M. and Berlekamp, E. R., A Lower Bound to the Distribution of Computations for Sequential Decoding, IEEE Transactions on Information Theory, vol. IT-13, pp. 167–174, 1967CrossRefGoogle Scholar
F. Jelinek, Probabilistic Information Theory, McGraw-Hill, New York, 1968
Jelinek, F., An Upper Bound on Moments of Sequential Decoding Effort, IEEE Transactions on Information Theory, vol. IT-15, pp. 140–149, 1969CrossRefGoogle Scholar
J. M. Jensen, On Decoding Doubly Extended Reed–Solomon Codes, Proceedings – 1995 IEEE International Symposium on Information, Whistler, BC, Canada, 1995
Johannesson, R., Robustly Optimal Rate One-Half Binary Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 464–468, 1975CrossRefGoogle Scholar
R. Johannesson and K. Sh. Zigangirov, Fundamentals of Convolutional Coding, IEEE Press, Piscataway, NJ, 1999
Justesen, J., A Class of Constructive Asymptotically Good Algebraic Codes, IEEE Transactions on Information Theory, vol. IT-18, pp. 652–656, 1972CrossRefGoogle Scholar
Kasahara, M., Sugiyama, Y., Hirasawa, S., and Namekawa, T., A New Class of Binary Codes Constructed on the Basis of BCH Codes, IEEE Transactions on Information Theory, vol. IT-21, pp. 582–585, 1975CrossRefGoogle Scholar
Kasami, T., Systematic Codes Using Binary Shift Register Sequences, Journal of the Information Processing Society of Japan, vol. 1, pp. 198–200, 1960Google Scholar
Kasami, T., Optimum Shortened Cyclic Codes for Burst-Error Correction, IEEE Transactions on Information Theory, vol. IT-9, pp. 105–109, 1963CrossRefGoogle Scholar
Kasami, T., A Decoding Procedure for Multiple-Error-Correcting Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 134–139, 1964CrossRefGoogle Scholar
Kasami, T. and Lin, S., The Binary Weight Distribution of the Extended (2m, 2m −4) Code of the Reed–Solomon Code overGF(2m) with Generator Polynomial (x−α)(x−α2)(x−α3), Linear Algebra and Its Applications, vol. 98, pp. 291–307, 1988CrossRefGoogle Scholar
Kasami, T. and Tokura, N., Some Remarks on BCH Bounds and Minimum Weights of Binary Primitive BCH Codes, IEEE Transactions on Information Theory, vol. IT-15, pp. 408–412, 1969CrossRefGoogle Scholar
T. Kasami, S. Lin, and W. W. Peterson, Some Results on Cyclic Codes Which are Invariant Under the Affine Group, Air Force Cambridge Research Labs Report, Cambridge, MA, 1966
Kasami, T., Lin, S., and Peterson, W. W., Some Results on Weight Distributions of BCH Codes, IEEE Transactions on Information Theory, vol. IT-12, p. 274, 1966Google Scholar
Kasami, T., Lin, S., and Peterson, W. W., New Generalizations of the Reed–Muller Codes – Part I: Primitive Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 189–199, 1968CrossRefGoogle Scholar
Kasami, T., Lin, S., and Peterson, W. W., Polynomial Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 807–814, 1968CrossRefGoogle Scholar
Z. Kiyasu, Research and Development Data No. 4, Electrical Communications Laboratory, Nippon Telegraph Corporation, Tokyo, Japan, 1953
Kolesnik, V. D. and Mironchikov, E. T., Some Cyclic Codes and a Scheme for Decoding by a Majority of Tests, Problemy Peredachi Informatsii, vol. 1, pp. 1–12, 1965Google Scholar
Kolesnik, V. D. and Mironchikov, E. T., Cyclic Reed–Muller Codes and Their Decoding, Problemy Peredachi Informatsii, vol. 4, pp. 15–19, 1968Google Scholar
Larsen, K. J., Short Convolutional Codes with Maximal Free Distance for Rate 1/2, 1/3, and 1/4, IEEE Transactions on Information Theory, vol. IT-19, pp. 371–372, 1973CrossRefGoogle Scholar
Laws, B. A. Jr and Rushforth, C. K., A Cellular-Array Multiplier forGF(2m), IEEE Transactions on Computers, vol. C-20, pp. 1573–1578, 1971CrossRefGoogle Scholar
Lee, P. J., There are Many Good Periodically Time-Varying Convolutional Codes, IEEE Transactions on Information Theory, vol. IT-35, pp. 460–463, 1989CrossRefGoogle Scholar
Lempel, A., Characterization and Synthesis of Self-Complementary Normal Bases in Finite Fields, Linear Algebra and Its Applications, vol. 98, pp. 331–346, 1988CrossRefGoogle Scholar
Lempel, A. and Winograd, S., A New Approach to Error-Correcting Codes, IEEE Transactions on Information Theory, vol. IT-23, pp. 503–508, 1977CrossRefGoogle Scholar
Lidl, R. and Niederreiter, H., Finite Fields: Encyclopedia of Mathematics and its Applications, vol. 20, Cambridge University Press, Cambridge, UK, 1984
Lin, S. and Markowsky, G., On a Class of One-Step Majority-Logic Decodable Cyclic Codes, IBM Journal of Research and Development, vol. 24, pp. 56–63, 1980CrossRefGoogle Scholar
Ma, J. H. and Wolf, J. K., On Tail-Biting Convolutional Codes, IEEE Transactions on Communications, vol. COM-34, pp. 1049–1053, 1988Google Scholar
MacWilliams, F. J., A Theorem on the Distribution of Weights in a Systematic Code, Bell System Technical Journal, vol. 42, pp. 79–94, 1963CrossRefGoogle Scholar
MacWilliams, F. J., Permutation Decoding of Systematic Codes, Bell System Technical Journal, vol. 43, pp. 485–505, 1964CrossRefGoogle Scholar
Mandelbaum, D. M., On Decoding of Reed–Solomon Codes, IEEE Transactions on Information Theory, vol. IT-17, pp. 707–712, 1971CrossRefGoogle Scholar
Mandelbaum, D. M., Decoding Beyond the Designed Distance for Certain Algebraic Codes, Information and Control, vol. 35, pp. 209–228, 1977CrossRefGoogle Scholar
Mandelbaum, D. M., Construction of Error-Correcting Codes by Interpolation, IEEE Transactions on Information Theory, vol. IT-25, pp. 27–35, 1979CrossRefGoogle Scholar
Mann, H. B., On the Number of Information Symbols in Bose–Chaudhuri Codes, Information and Control, vol. 5, pp. 153–162, 1962CrossRefGoogle Scholar
J. L. Massey, Threshold Decoding, MIT Press, Cambridge, MA, 1963
Massey, J. L., Shift-Register Synthesis and BCH Decoding, IEEE Transactions on Information Theory, vol. IT-15, pp. 122–127, 1969CrossRefGoogle Scholar
J. L. Massey, Error bounds for tree codes, trellis codes and convolutional codes with encoding and decoding procedures, in Coding and Complexity, G. Longo, editor, Springer-Verlag, New York, NY, 1975
J. L. Massey, Coding theory, Chapter 16 of Handbook of Applicable Mathematics, Volume V, Part B of Combinatorics and Geometry, W. Ledermann and S. Vajda, editors, Wiley, Chichester and New York, NY, 1985
Massey, J. L. and Sain, M. K., Inverses of Linear Sequential Circuits, IEEE Transactions on Computers, vol. C-17, pp. 330–337, 1968CrossRefGoogle Scholar
Mattson, H. F. and Solomon, G., A New Treatment of Bose–Chaudhuri Codes, Journal of the Society of Industrial and Applied Mathematics, vol. 9, pp. 654–669, 1961CrossRefGoogle Scholar
U. Maurer and R. Viscardi, Running-Key Generators with Memory in the Nonlinear Combining Function, Diploma Thesis, Swiss Federal Institute of Technology, Zurich, 1984
R. J. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer, Boston, MA, 1987
R. J. McEliece, The algebraic theory of convolutional codes, in Handbook of Coding Theory, pp. 1065–1138, V. S. Pless and W. C. Huffman, editors, Elsevier, Amsterdam, 1998
McEliece, R. J., MacKay, D. J. C., and Cheng, J. F., Turbo Decoding as an Instance of Pearl's ‘Belief Propagation’ Algorithm, IEEE Journal on Selected Areas in Communication, vol. SAC-16, pp. 140–152, 1998CrossRefGoogle Scholar
McEliece, R. J. and Onyszchuk, I., The Analysis of Convolutional Codes via the Extended Smith Algorithm, Jet Propulsion Laboratory TDA Progress Report, vol. 42–112, pp. 22–30, 1993Google Scholar
McEliece, R. J., Rodemich, E. R., Rumsey, H. Jr, and Welch, L. R., New Upper Bounds on the Rate of a Code Via the Delsarte–MacWilliams Inequalities, IEEE Transactions on Information Theory, vol. IT-23, pp. 157–166, 1977CrossRefGoogle Scholar
Meggitt, J. E., Error-Correcting Codes for Correcting Bursts of Errors, IBM Journal of Research and Development, vol. 4, pp. 329–334, 1960CrossRefGoogle Scholar
Meggitt, J. E., Error-Correcting Codes and Their Implementation, IRE Transactions on Information Theory, vol. IT-7, pp. 232–244, 1961Google Scholar
A. Michelson, A Fast Transform in Some Galois Fields and an Application to Decoding Reed-Solomon Codes, IEEE Abstracts of Papers – IEEE International Symposium on Information Theory, Ronneby, Sweden, 1976
M. E. Mitchell, Error-Trap Decoding of Cyclic Codes, G.E. Report No. 62MCD3, General Electric Military Communications Department, Oklahoma City, OK, 1962
Morii, M., Kasahara, M., and Whiting, D. L., Efficient Bit-Serial Multiplication and the Discrete-Time Wiener–Hopf Equation over Finite Fields, IEEE Transactions on Information Theory, vol. IT-35, pp. 1177–1183, 1989CrossRefGoogle Scholar
Muder, D. J., Minimal Trellises for Block Codes, IEEE Transactions on Information Theory, vol. IT-34, pp. 1049–1053, 1988CrossRefGoogle Scholar
Muller, D. E., Application of Boolean Algebra to Switching Circuit Design and to Error Detection, IRE Transactions on Electronic Computers, vol. EC-3, pp. 6–12, 1954Google Scholar
J. P. Odenwalder, Optimal Decoding of Convolutional Codes, Ph.D. Dissertation, University of California at Los Angeles, Los Angeles, CA, 1970
J. K. Omura and J. L. Massey, Computational Method and Apparatus for Finite Field Arithmetic, U.S. Patent 4 587 627, May 6, 1986 (Filed September 14, 1982)
Paaske, E., Short Binary Convolutional Codes with Maximal Free Distance for Rates 2/3, and 3/4, IEEE Transactions on Information Theory, vol. IT-20, pp. 683–689, 1974CrossRefGoogle Scholar
R. H. Paschburg, Software Implementation of Error-Correcting Codes, M.S. Thesis, University of Illinois, Urbana, IL, 1974
Peterson, W. W., Encoding and Error-Correction Procedures for the Bose–Chaudhuri Codes, IRE Transactions on Information Theory, vol. IT-6, pp. 459–470, 1960CrossRefGoogle Scholar
W. W. Peterson, Error Correcting Codes, MIT Press, Cambridge, MA, and Wiley, New York, NY, 1961
W. W. Peterson and E. J. Weldon, Jr., Error Correcting Codes, Second Edition, MIT Press, Cambridge, MA, 1972
Pless, V., Power Moment Identities on Weight Distributions in Error Correcting Codes, Information and Control, vol. 6, pp. 147–152, 1963CrossRefGoogle Scholar
Pless, V. S., On the Uniqueness of the Golay Codes, Journal of Combinatoric Theory, vol. 5, pp. 215–228, 1968CrossRefGoogle Scholar
Plotkin, M., Binary Codes with Specified Minimum Distances, IEEE Transactions on Information Theory, vol. IT-6, pp. 445–450, 1960CrossRefGoogle Scholar
Pollard, J. M., The Fast Fourier Transform in a Finite Field, Mathematics of Computation, vol. 25, pp. 365–374, 1971CrossRefGoogle Scholar
E. Prange, Cyclic Error-Correcting Codes in Two Symbols, AFCRC-TN-57–103, Air Force Cambridge Research Center, Cambridge, MA, 1957
E. Prange, Some Cyclic Error-Correcting Codes with Simple Decoding Algorithms, AFCRC-TN-58–156, Air Force Cambridge Research Center, Bedford, MA, 1958
Reed, I. S., A Class of Multiple-Error-Correcting Codes and the Decoding Scheme, IRE Transactions on Information Theory, vol. IT-4, pp. 38–49, 1954Google Scholar
Reed, I. S. and Solomon, G., Polynomial Codes over Certain Finite Fields, Journal of the Society of Industrial and Applied Mathematics, vol. 8, pp. 300–304, 1960CrossRefGoogle Scholar
Retter, C. T., The Average Binary Weight-Enumerator for a Class of Generalized Reed–Solomon Codes, IEEE Transactions on Information Theory, vol. IT-37, pp. 346–349, 1991CrossRefGoogle Scholar
Robinson, J. P. and Bernstein, A. J., A Class of Recurrent Codes with Limited Error Propagation, IEEE Transactions on Information Theory, vol. IT-13, pp. 106–113, 1967CrossRefGoogle Scholar
L. D. Rudolph, Geometric Configuration and Majority-Logic Decodable Codes, M.E.E. Thesis, University of Oklahoma, Norman, OK, 1964
Rudolph, L. D., A Class of Majority-Logic Decodable Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 305–307, 1967CrossRefGoogle Scholar
Rudolph, L. and Mitchell, M. E., Implementation of Decoders for Cyclic Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 259–260, 1964CrossRefGoogle Scholar
Sarwate, D. V. and Morrison, R. D., Decoder Malfunction in BCH Decoders, IEEE Transactions on Information Theory, vol. IT-36, pp. 884–889, 1990CrossRefGoogle Scholar
Sarwate, D. V. and Shanbhag, N. R., High-Speed Architecture for Reed–Solomon Decoders, IEEE Transactions on VLSI Systems, vol. VLSI-9, pp. 641–655, 2001CrossRefGoogle Scholar
Savage, J. E., Minimum Distance Estimates of the Performance of Sequential Decoding, IEEE Transactions on Information Theory, vol. IT-15, pp. 128–140, 1969CrossRefGoogle Scholar
T. Schaub, A Linear Complexity Approach to Cyclic Codes, Doctor of Technical Sciences Dissertation, Swiss Federal Institute of Technology, Zurich, 1988
Schönheim, J., On Linear and Nonlinear Single-Error-Correctingq-nary Perfect Codes, Information and Control, vol. 12, pp. 23–26, 1968CrossRefGoogle Scholar
C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol. 27, pp. 379–423, 1948 (Part I), pp. 623–656 (Part II) reprinted in book form with postscript by W. Weaver, University of Illinois Press, Urbana, IL, 1949; Anniversary Edition, 1998
Shao, H. M., Truong, T. K., Deutsch, L. J., Yuen, J. H., and Reed, I. S., A VLSI Design of a Pipeline Reed–Solomon Decoder, IEEE Transactions on Computers, vol. C-34, pp. 393–403, 1985CrossRefGoogle ScholarPubMed
Singleton, R. C., Maximum Distanceq-nary Codes, IEEE Transactions on Information Theory, vol. IT-10, pp. 116–118, 1964CrossRefGoogle Scholar
Slepian, D., A Class of Binary Signaling Alphabets, Bell System Technical Journal, vol. 35, pp. 203–234, 1956CrossRefGoogle Scholar
Slepian, D., Some Further Study of Group Codes, Bell System Technical Journal, vol. 39, pp. 1219–1252, 1960CrossRefGoogle Scholar
Sloane, N. J. A., Reddy, S. M., and Chen, C. L., New Binary Codes, IEEE Transactions on Information Theory, vol. IT-18, pp. 503–510, 1972CrossRefGoogle Scholar
Smith, H. J. S., On Systems of Linear Indeterminant Equations and Congruences, Philosophical Transactions of the Royal Society, vol. 151, pp. 293–326, 1861CrossRefGoogle Scholar
Solomon, G. and Tilborg, H. C. A., A Connection Between Block and Convolutional Codes, SIAM Journal of Applied Mathematics, vol. 37, pp. 358–369, 1979CrossRefGoogle Scholar
G. Strang, Linear Algebra and Its Applications, Second Edition, Academic Press, New York, NY, 1980
Sudan, M., Decoding of Reed–Solomon Codes Beyond the Error-Correction Bound, Journal of Complexity, vol. 13, pp. 180–183, 1997CrossRefGoogle Scholar
M. Sudan, Decoding of Reed–Solomon Codes Beyond the Error-Correction Diameter, Proceedings of the Thirty-Fifth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, IL, 1997
Sugiyama, Y., Kasahara, M., Hirasawa, S., and Namekawa, T., A Method for Solving Key Equation for Decoding Goppa Codes, Information and Control, vol. 27, pp. 87–99, 1975CrossRefGoogle Scholar
Tanner, R. M., A Recursive Approach to Low-Complexity Codes, IEEE Transactions on Information Theory, vol. IT-27, pp. 535–547, 1981Google Scholar
R. M. Thrall and L. Tornheim, Vector Spaces and Matrices, Wiley, New York, NY, 1957
A. Tietäväinen, A Short Proof for the Nonexistence of Unknown Perfect Codes over GF(q), q《2, Annales Acad. Scient. Fennicae, Ser. A., no. 580, pp. 1–6, 1974
Tsfasman, M. A., Vladut, S. G., and Zink, Th., Modular Curves, Shimura Curves, and Goppa Codes Better Than the Varshamov–Gilbert Bound, Math. Nachr., vol. 104, pp. 13–28, 1982Google Scholar
Ungerboeck, G., Channel Coding with Multilevel Phase Signals, IEEE Transactions on Information Theory, vol. IT-28, pp. 55–67, 1982CrossRefGoogle Scholar
B. L. Van der Waerden, Modern Algebra (two volumes), translated by F. Blum and T. J. Benac, Frederick Ungar, New York, NY, 1950 and 1953
Lint, J. H., A Survey of Perfect Codes, Rocky Mountain Journal of Mathematics, vol. 5, pp. 199–224, 1975CrossRefGoogle Scholar
Vanderhorst, J. and Berger, T., Complete Decoding of Triple-Error-Correcting Binary BCH Codes, IEEE Transactions on Information Theory, vol. IT-22, pp. 138–147, 1976CrossRefGoogle Scholar
A. Vardy, Trellis Structure of Codes, in Handbook of Coding Theory, editors, V. S. Pless and W. C. Huffman, Elsevier Science, Amsterdam, 1999
Varshamov, R. R., Estimate of the Number of Signals in Error Correcting Codes, Doklady Akad. Nauk SSSR, vol. 117, pp. 739–741, 1957Google Scholar
Vasilýev, Y. L., On Nongroup Close-Packed Codes, Problemi Cybernetica, vol. 8, pp. 337–339, 1962Google Scholar
Viterbi, A. J., Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm, IEEE Transactions on Information Theory, vol. IT-13, pp. 260–269, 1967CrossRefGoogle Scholar
A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding, McGraw-Hill, 1979
L. R. Welch and E. R. Berlekamp, Error Correction for Algebraic Block Codes, US Patent 4 633 470, 1983
Welch, L. R. and Scholtz, R. A., Continued Fractions and Berlekamp's Algorithm, IEEE Transactions on Information Theory, vol. IT-25, pp. 19–27, 1979CrossRefGoogle Scholar
E. J. Weldon, Jr., euclidean Geometry Cyclic Codes, Proceedings of the Symposium on Combinatorial Mathematics, University of North Carolina, Chapel Hill, NC, 1967
Weldon, E. J. Jr, New Generalizations of the Reed–Muller Codes – Part II: Non-Primitive Codes, IEEE Transactions on Information Theory, vol. IT-14, pp. 199–206, 1968CrossRefGoogle Scholar
N. Wiberg, Codes Depending on General Graphs, Doctor of Philosophy Dissertation, Department of Electrical Engineering, University of Linkoping, Sweden, 1996
Wiberg, N., Loeliger, H. A., and Kötter, R., Codes and Iterative Decoding on General Graphs, European Transactions on Telecommunications, vol. 6, pp. 513–526, 1995CrossRefGoogle Scholar
Willett, M., Arithmetic in a Finite Field, Mathematics of Computation, vol. 35, pp. 1353–1359, 1980CrossRefGoogle Scholar
Wolf, J. K., Adding Two Information Symbols to Certain Nonbinary BCH Codes and Some Applications, Bell System Technical Journal, vol. 48, pp. 2405–2424, 1969CrossRefGoogle Scholar
Wolf, J. K., Efficient Maximum-Likelihood Decoding of Linear Block Codes Using a Trellis, IEEE Transactions on Information Theory, vol. 24, pp. 76–80, 1978CrossRefGoogle Scholar
Wozencraft, J. M., Sequential Decoding for Reliable Communication, 1957 National IRE Convention Record, vol. 5, Part 2, pp. 11–25, 1957Google Scholar
J. M. Wozencraft and B. Reiffen, Sequential Decoding, MIT Press, Cambridge, MA, 1961
W. W. Wu, New Convolutional Codes, IEEE Transactions on Communication Theory, Part I, vol. COM-23, pp. 942–956, 1975; Part II, vol. COM-24, pp. 19–33, 1976; Part III, vol. COM-24, pp. 946–955, 1976
Wyner, A. D. and Ash, R. B., Analysis of Recurrent Codes, IEEE Transactions on Information Theory, vol. IT-9, pp. 143–156, 1963CrossRefGoogle Scholar
N. Zierler, On a Variation of the First Order Reed–Muller Codes, Massachusetts Institute of Technology Lincoln Laboratory Group Report 34–80, Lexington, MA, 1958
Zigangirov, K., Sequential Decoding Procedures, Problemy Peredachi Informatsii, vol. 2, pp. 13–25, 1966.Google Scholar

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  • Bibliography
  • Richard E. Blahut, University of Illinois, Urbana-Champaign
  • Book: Algebraic Codes for Data Transmission
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511800467.016
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  • Bibliography
  • Richard E. Blahut, University of Illinois, Urbana-Champaign
  • Book: Algebraic Codes for Data Transmission
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511800467.016
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  • Bibliography
  • Richard E. Blahut, University of Illinois, Urbana-Champaign
  • Book: Algebraic Codes for Data Transmission
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511800467.016
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