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

doi:10.1017/CBO9780511525988

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.

‘… a state-of-the-art account of the area of finite fields and their applications.’

Source: L’Enseignement Mathématique

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
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Conference Participants
pp ix-xx
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Factorizations over finite fields
pp 1-22
- By Shreeram S Abhyankar
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Class number in totally imaginary extensions of totally real function fields
pp 23-30
- By Yves Aubry
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Automorphism groups and permutation groups of affine-invariant codes
pp 31-46
- By Thierry P Berger
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A construction of bent functions
pp 47-58
- By Claude Carlet
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Monodromy groups of classical families over finite fields
pp 59-68
- By Stephen D Cohen, Rex W Matthews
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Wan's bound for value sets of polynomials
pp 69-72
- By Thomas W Cusick, Peter Müller
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Comparative implementations of Berlekamp's and Niederreitor's polynomial factorization algorithms
pp 73-84
- By Peter Fleischmann, Peter Roelse
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On the minimal polynomials for certain Gauss periods over finite fields
pp 85-96
- By S Gurak
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Completely free elements
pp 97-108
- By Dirk Hachenberger
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Exponential sums over Galois rings and their applications
pp 109-128
- By T Helleseth, P V Kumar, A G Shanbhag
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Maximal sets of mutually orthogonal Latin squares
pp 129-154
- By Dieter Jungnickel
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Examples of small hybrid sums
pp 155-162
- By Jyrki Lahtonen
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Cellular automata, substitutions and factorization of polynomials over finite fields
pp 163-180
- By Ehler Lange
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A new class of two weight codes
pp 181-188
- By Philippe Langevin
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Construction of digital (t, m, s)-nets from linear codes
pp 189-208
- By K Mark Lawrence, Arijit Mahalanabis, Gary L Mullen, Wolfgang Ch Schmid
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A family of exceptional polynomials in characteristic three
pp 209-218
- By H W Lenstra, Jr, M Zieve
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Estimates of character sums arising from finite upper half planes
pp 219-228
- By Wen-Ching Winnie Li
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Carmichael-Carlitz polynomials and Fermat-Carlitz quotients
pp 229-242
- By Véronique Mauduit
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Open problems and conjectures in finite fields
pp 243-268
- By Gary L Mullen, Igor Shparlinski
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Quasirandom points and global function fields
pp 269-296
- By Harald Niederreiter, Chaoping Xing
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Use characteristic sets to decode cyclic codes up to actual minimum distance
pp 297-312
- By Chunming Rong, Tor Helleseth
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Approximate constructions in finite fields
pp 313-332
- By Igor Shparlinski
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Periodicity properties of kth order linear recurrences whose characteristic polynomial splits completely over a finite field, II
pp 333-348
- By Lawrence Somer
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Factoring cyclotomic polynomials over large finite fields
pp 349-354
- By Greg Stein
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Character sums and coding theory
pp 355-378
- By Serguei A Stepanov
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L-functions of algebraic varieties over finite fields: rationality, meromorphy and entireness
pp 379-394
- By Daqing Wan
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Finite Fields and Applications

Proceedings of the Third International Conference, Glasgow, July 1995

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