Contemporary Mathematics 1994; 402 pp; softcover Volume: 168 ISBN10: 0821851837 ISBN13: 9780821851838 List Price: US$79 Member Price: US$63.20 Order Code: CONM/168
 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  P. Charpin  Tools for coset weight enumerators of some codes
 X. Chen, I. S. Reed, T. Helleseth, and T. K. Truong  Algebraic decoding of cyclic codes: A polynomial ideal point of view
 S. D. Cohen  Polynomial factorisation, graphs, designs and codes
 R. Evans  Character sums as orthogonal eigenfunctions of adjacency operators for Cayley graphs
 M. Fellows and N. Koblitz  Combinatorial cryptosystems galore!
 R. Figueroa, P. M. Salzberg, and P. J.S. Shiue  A family of cryptosystems based on combinatorial properties of finite geometries
 M. D. Fried  Global construction of general exceptional covers
 S. Gao and J. von zur Gathen  Berlekamp's and Niederreiter's polynomial factorization algorithms
 R. Göttfert and H. Niederreiter  HasseTeichmüller derivatives and products of linear recurring sequences
 S. Gurak  Factors of period polynomials for finite fields, II
 N. Hamada and T. Helleseth  A characterization of some ternary codes meeting the Griesmer bound
 J. W. P. Hirschfeld and R. Shaw  Projective geometry codes over prime fields
 K. Huber  Codes over EisensteinJacobi integers
 H. Kiechle  Points on Fermat curves over finite fields
 A. Knopfmacher, J. Knopfmacher, and R. Warlimont  Lengths of factorizations for polynomials over a finite field
 J. Kuang  A note on Weil representation of \(\mathrm {SL}_2({\mathbb F\!}_q)\) and SotoAndrade sums
 P. Langevin  Some sequences with good autocorrelation properties
 H. Lu  Pellian equation conjecture and absolutely nonsingular projective varieties over a finite fieldHecke operator and Pellian equation conjecture (IV)
 R. Matthews  Strong pseudoprimes and generalized Carmichael numbers
 O. Moreno and V. A. Zinoviev  Transformations of \(4\)regular graphs and equations over finite fields of ChevalleyWarning type
 P. Müller  New examples of exceptional polynomials
 H. Niederreiter  New deterministic factorization algorithms for polynomials over finite fields
 A. M. Odlyzko  Discrete logarithms and smooth polynomials
 V. Pless  Parents, children, neighbors and the shadow
 M. Qu and S. A. Vanstone  The knapsack problem in cryptography
 A. Scheerhorn  Iterated constructions of normal bases over finite fields
 L. Somer  Periodicity properties of \(k\) th order linear recurrences whose characteristic polynomial splits completely over a finite field, I
 H. Y. Song and S. W. Golomb  Generalized WelchCostas sequences and their application to Vatican arrays
 S. J. Suchower  Nonisomorphic complete sets of \(F\)rectangles with varying numbers of symbols
 S. Tezuka and M. Fushimi  A method of designing cellular automata as pseudorandom number generators for builtin selftest for VLSI
 C. E. Trimble  Finite ring sums from \(p\)adic K Bessel functions
 P. T. Young  On the GrossKoblitz formula
 J. Wolfmann  New results on diagonal equations over finite fields from cyclic codes
 K. Huber, I. H. Morgan, G. L. Mullen, H. Niederreiter, A. Odlyzko, J. van Tilburg, and D. Wan  Open problems and conjectures
