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Finite Fields and Applications

Finite Fields and Applications
Proceedings of the Third International Conference, Glasgow, July 1995

Part of London Mathematical Society Lecture Note Series

S. Abhyankar, Y. Aubry, T. P. Berger, C. Carlet, S. Cohen, R. W. Matthews, T. W. Cusick, P. Müller, P. Fleischmann, P. Roelse, S. Gurak, D. Hachenberger, T. Helleseth, P. V. Kumar, A. G. Shanbhag, A. Mahalanabis, W. Schmid, D. Jungnickel, J. Lahtonen, E. Lange, P. Langevin, K. M. Lawrence, H. W. Lenstra, M. Zieve, W. C. Li, V. Mauduit, G. L. Mullen, I. Shparlinski, H. Niederreiter, C. Xing, C. Rong, L. Somer, G. Stein, S. A. Stepanov, D. Wan, P.T. Young
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  • Date Published: October 1996
  • availability: Available
  • format: Paperback
  • isbn: 9780521567367

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  • Finite fields are algebraic structures in which there is much research interest and they have been shown to have a wide range of applications. These proceedings give a state-of-the-art account of the area of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. These also demonstrate inter-connections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.

    • Contributions from best people
    • Up-to-date research
    • Of interest to algebraists, number theorists and cryptologists
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    Reviews & endorsements

    '… a state-of-the-art account of the area of finite fields and their applications.' L'Enseignement Mathématique

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    Product details

    • Date Published: October 1996
    • format: Paperback
    • isbn: 9780521567367
    • length: 424 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.62kg
    • availability: Available
  • Table of Contents

    1. Factorizations over finite fields Abhyankar
    2. Class number in totally imaginary extensions Aubry
    3. Automorphism groups and permutation groups Berger
    4. A construction of bent functions Carlet
    5. Monodromy groups of classical families Cohen and Matthews
    6. Wan's bound Cusick and Müller
    7. Factorization
    8. Algorithms Fleischmann and Roelse
    9. Minimal polynomials for certain Gauss periods Gurak
    10. Completely free elements Hachenberger
    11. Exponential sums over Galois rings Helleseth et al.
    12. Mutually orthogonal Latin squares Jungnickel
    13. Examples of small hybrid sums Lahtonen
    14. Cellular automata Lange
    15. A new class of two weight code Langevin et al
    16. Construction of digital (t,m,s)-nets Lawrence et al
    17. A family of exceptional polynomials Lenstra and Zieve
    18. Estimates of character sums Li
    19. Carmichael-Carlitz polynomials Mauduit
    20. Open problems and conjectures Mullen and Shparlinski
    21. Quasirandom points Niederreiter and Xing
    22. Character sets to decode cyclic codes Rong and Helleseth
    23. Approximate constructions in finite fields Shparlinski
    24. Periodicity properties of linear recurrences Somer
    25. Factoring cyclotomic polynomials Stein
    26. Character sums and coding theory Stepanov
    27. L-functions of algebraic varieties Wan
    28. Generalizations of R'edei functions Young.

  • Editors

    S. Cohen, University of Glasgow

    H. Niederreiter, National University of Singapore

    Contributors

    S. Abhyankar, Y. Aubry, T. P. Berger, C. Carlet, S. Cohen, R. W. Matthews, T. W. Cusick, P. Müller, P. Fleischmann, P. Roelse, S. Gurak, D. Hachenberger, T. Helleseth, P. V. Kumar, A. G. Shanbhag, A. Mahalanabis, W. Schmid, D. Jungnickel, J. Lahtonen, E. Lange, P. Langevin, K. M. Lawrence, H. W. Lenstra, M. Zieve, W. C. Li, V. Mauduit, G. L. Mullen, I. Shparlinski, H. Niederreiter, C. Xing, C. Rong, L. Somer, G. Stein, S. A. Stepanov, D. Wan, P.T. Young

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