Finite Fields

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.

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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