Finite Fields

by International Conference on Finite Fields: Theory, Applications, and Algorithms (4th : 1997 : University of Waterloo)

• ISBN13: 9780821808177
• ISBN10: 0821808176
• Format: Paperback
• Copyright: 1998-10-01
• Publisher: Amer Mathematical Society

Summary

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 Fourth International Conference on "Finite Fields: Theory, Applications, and Algorithms" was held at the University of Waterloo in August 1997. The conference drew workers in theoretical, applied, and algorithmic finite field theory. This volume presents the referred proceedings. 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.

Table of Contents

Computing composed products of polynomials

Actions of linearized polynomials on the algebraic closure of a finite field

On degree bounds for invariant rings of finite groups over finite fields

Irreducible polynomials of given forms

An application of Galois calculus to $\mathbb {F}_t[t]$

Composition behavior of sub-linearised polynomials over a finite field

Kernels and defaults

global function fields with many rational places and their applications

Traces of roots of unity over prime fields

The fermat curve in charcteristic $p$

Computing zeta functions over finite fields

Cyclic alternant codes induced by an automorphism of a GRS code

On Kerdock codes

Permutation group of the $q$-ary image of some $q^m$-ary cyclic codes

The number of solutions to a system of equations and spectra of codes

The LD probable prime test

Carmichael numbers and Lucas tests

On the state complexity of some long codes

ID-based key distribution system over an elliptic curve

Symmetric sets of curves and combinatorial arrays

Weight functions and the extension theorem for linear codes over finite rings

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