Finite Fields : Theory, Applications, and Algorithms.

Intro -- Contents -- Preface -- Contributors -- Conference Participants -- 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-Teichmiiller 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 SL2(Fq) 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 kth 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.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.