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Finite Fields: Theory, Applications, and Algorithms
Edited by: Gary L. Mullen and Peter Jau-Shyong Shiue

Contemporary Mathematics
1994; 402 pp; softcover
Volume: 168
ISBN-10: 0-8218-5183-7
ISBN-13: 978-0-8218-5183-8
List Price: US$79
Member Price: US$63.20
Order Code: CONM/168
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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.


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 -- Hasse-Teichmüller 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 Eisenstein-Jacobi 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 Soto-Andrade sums
  • P. Langevin -- Some sequences with good autocorrelation properties
  • H. Lu -- Pellian equation conjecture and absolutely nonsingular projective varieties over a finite field--Hecke 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 Chevalley-Warning 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 Welch-Costas 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 built-in self-test for VLSI
  • C. E. Trimble -- Finite ring sums from \(p\)-adic K -Bessel functions
  • P. T. Young -- On the Gross-Koblitz 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
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