Finite Fields

by International Conference on Finite Fields: Theory, Applications, and Algorithms (4th : 1997 : University of Waterloo)

• ISBN13: 9780821851838
• ISBN10: 0821851837
• Format: Paperback
• Copyright: 1994-11-01
• Publisher: Amer Mathematical Society

Summary

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.

Table of Contents

Tools for coset weight enumerators of some codes

Algebraic decoding of cyclic codes: A polynomial ideal point of view

Polynomial factorisation, graphs, designs and codes

Character sums as orthogonal eigenfunctions of adjacency operators for Cayley graphs

Combinatorial cryptosystems galore!

A family of cryptosystems based on combinatorial properties of finite geometries

global construction of general exceptional covers

Berlekamp's and Niederreiter's polynomial factorization algorithms

Hasse-Teichmuller derivatives and products of linear recurring sequences

Factors of period polynomials for finite fields, II

A characterization of some ternary codes meeting the Griesmer bound

Projective geometry codes over prime fields

Codes over Eisenstein-Jacobi integers

Points on Fermat curves over finite fields

Lengths of factorizations for polynomials over a finite field

A note on Weil representation of $\mathrm {SL}_2({\mathbb F\!}_q)$ and Soto-Andrade sums

Some sequences with good autocorrelation properties

Pellian equation conjecture and absolutely nonsingular projective varieties over a finite field–Hecke operator and Pellian equation conjecture (IV)

Strong pseudoprimes and generalized Carmichael numbers

Transformations of $4$-regular graphs and equations over finite fields of Chevalley-Warning type

New examples of exceptional polynomials

New deterministic factorization algorithms for polynomials over finite fields

Discrete logarithms and smooth polynomials

Parents, children, neighbors and the shadow

The knapsack problem in cryptography

Iterated constructions of normal bases over finite fields

Periodicity properties of $k$ th order linear recurrences whose characteristic polynomial splits completely over a finite field, I

Generalized Welch-Costas sequences and their application to Vatican arrays

Nonisomorphic complete sets of $F$-rectangles with varying numbers of symbols

A method of designing cellular automata as pseudorandom number generators for built-in self-test for VLSI

Finite ring sums from $p$-adic K -Bessel functions

On the Gross-Koblitz formula

New results on diagonal equations over finite fields from cyclic codes

Open problems and conjectures

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