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Finite Fields: Theory, Applications and Algorithms
Edited by: Ronald C. Mullin, University of Waterloo, ON, Canada, and Gary L. Mullen, Pennsylvania State University, University Park, PA

Contemporary Mathematics
1999; 243 pp; softcover
Volume: 225
ISBN-10: 0-8218-0817-6
ISBN-13: 978-0-8218-0817-7
List Price: US$63
Member Price: US$50.40
Order Code: CONM/225
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The Fourth International Conference on "Finite Fields: Theory, Applications, and Algorithms" was held at the University of Waterloo in August 1997. This volume presents the refereed proceedings.

Because of its applications in so many diverse areas, finite fields continues to grow in importance in modern mathematics. Finite fields now play particularly important roles in number theory, algebra, and algebraic geometry. They also play a crucial role in computer science, statistics, and engineering. Areas of application include but are not limited to algebraic coding theory, cryptology, and combinatorial design theory. Computational and algorithmic aspects of finite field problems are also growing in significance.

The conference drew workers in theoretical, applied, and algorithmic finite field theory. All papers were refereed. They are loosely classified as theoretical and applied and are listed under these general headings. The work contains up-to-date results from leading experts in the field.


Graduate students, pure and applied mathematicians, computer scientists, and communications engineers working in error-correcting codes and public key cryptography.

Table of Contents

  • J. V. Brawley, S. Gao, and D. Mills -- Computing composed products of polynomials
  • S. D. Cohen and D. Hachenberger -- Actions of linearized polynomials on the algebraic closure of a finite field
  • P. Fleischmann and W. Lempken -- On degree bounds for invariant rings of finite groups over finite fields
  • S. Gao, J. Howell, and D. Panario -- Irreducible polynomials of given forms
  • Y. Hellegouarch -- An application of Galois calculus to \(\mathbb {F}_t[t]\)
  • M. Henderson and R. Matthews -- Composition behavior of sub-linearised polynomials over a finite field
  • P. Langevin and P. Solé -- Kernels and defaults
  • H. Niederreiter and C. Xing -- Global function fields with many rational places and their applications
  • G. Stein -- Traces of roots of unity over prime fields
  • H. Stichtenoth -- The fermat curve in charcteristic \(p\)
  • D. Wan -- Computing zeta functions over finite fields
  • T. P. Berger -- Cyclic alternant codes induced by an automorphism of a GRS code
  • C. Carlet -- On Kerdock codes
  • J. Lacan and E. Delpeyroux -- Permutation group of the \(q\)-ary image of some \(q^m\)-ary cyclic codes
  • O. Keren and S. Litsyn -- The number of solutions to a system of equations and spectra of codes
  • W. More -- The LD probable prime test
  • S. M. S. Müller -- Carmichael numbers and Lucas tests
  • T. Blackmore and G. Norton -- On the state complexity of some long codes
  • H. Sakazaki, E. Okamoto, and M. Mambo -- ID-based key distribution system over an elliptic curve
  • R. Fuji-Hara and S. Shinohara -- Symmetric sets of curves and combinatorial arrays
  • J. A. Wood -- Weight functions and the extension theorem for linear codes over finite rings
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