**Contemporary Mathematics**

Volume: 168;
1994;
402 pp;
Softcover

MSC: Primary 11;
Secondary 05; 94

Print ISBN: 978-0-8218-5183-8

Product Code: CONM/168

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

**Electronic ISBN: 978-0-8218-7759-3
Product Code: CONM/168.E**

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

# Finite Fields: Theory, Applications, and Algorithms

Share this page *Edited by *
*Gary L. Mullen; Peter Jau-Shyong Shiue*

Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.

#### Readership

Graduate students and researchers in the theory and application of finite fields. More generally, students and researchers in algebra, number theory, combinatorial design theory, coding theory, and cryptology.

# Table of Contents

## Finite Fields: Theory, Applications, and Algorithms

- Contents vii8 free
- Preface xi12 free
- Contributors xiii14 free
- Conference Participants xix20 free
- Tools for coset weight enumerators of some codes 132 free
- Algebraic decoding of cyclic codes: A polynomial ideal point of view 1546
- Polynomial factorisation, graphs, designs and codes 2354
- Character sums as orthogonal eigenfunctions of adjacency operators for Cayley graphs 3364
- Combinatorial cryptosystems galore! 5182
- A family of cryptosystems based on combinatorial properties of finite geometries 6394
- Global construction of general exceptional covers 69100
- Berlekamp's and Niederreiter's polynomial factorization algorithms 101132
- Hasse-Teichmiiller derivatives and products of linear recurring sequences 117148
- Factors of period polynomials for finite fields, II 127158
- A characterization of some ternary codes meeting the Griesmer bound 139170
- Projective geometry codes over prime fields 151182
- Codes over Eisenstein-Jacobi integers 165196
- Points on Fermat curves over finite fields 181212
- Lengths of factorizations for polynomials over a finite field 185216
- A note on Weil representation of SL2(Fq) and Soto-Andrade sums 207238
- Some sequences with good autocorrelation properties 213244
- Pellian equation conjecture and absolutely nonsingular projective varieties over a finite field–Hecke operator and Pellian equation conjecture (IV) 217248
- Strong pseudoprimes and generalized Carmichael numbers 227258
- Transformations of 4-regular graphs and equations over finite fields of Chevalley-Warning type 235266
- New examples of exceptional polynomials 245276
- New deterministic factorization algorithms for polynomials over finite fields 251282
- Discrete logarithms and smooth polynomials 269300
- Parents, children, neighbors and the shadow 279310
- The knapsack problem in cryptography 291322
- Iterated constructions of normal bases over finite fields 309340
- Periodicity properties of kth order linear recurrences whose characteristic polynomial splits completely over a finite field, I 327358
- Generalized Welch-Costas sequences and their application to Vatican arrays 341372
- Nonisomorphic complete sets of F-rectangles with varying numbers of symbols 353384
- A method of designing cellular automata as pseudorandom number generators for built-in self-test for VLSI 363394
- Finite ring sums from p-adic K-Bessel functions 369400
- On the Gross-Koblitz formula 379410
- New results on diagonal equations over finite fields from cyclic codes 387418
- Open problems and conjectures 397428