Finite Fields and Applications

by Mullen, Gary L.; Panario, Daniel; Shparlinski, Igor E.

• ISBN13: 9780821843093
• ISBN10: 0821843095
• Format: Paperback
• Copyright: 2008-08-01
• Publisher: Amer Mathematical Society

Summary

This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.

Table of Contents

Analysis and optimization of elliptic-curve single-scalar multiplication

On influences of Boolean variables and their computation

Subsequences of Sidelnikov sequences

A multi-level blocking distinct-degree factorization algorithm

New bounds on some parameters in the Waring problem for polynomials over a finite field

Dickson polynomial permutations

Ring theoretic study of linear codes using additive polynomials

Toward a complete twin primes theorem for polynomials over finite fields

On the distribution of the elliptic curve power generator

Discrete logarithms in curves over finite fields

Some remarks on the Hasse-Arf theorem

Character sums for sequences of iterations of Dickson polynomials

What can be used instead of a Barker sequence?

Order dividing extension fields and the root computation problem

Kasami bent functions are not equivalent to their duals

Reduced linear modular systems

Cocyclic Butson Hadamard matrices and codes over $\mathbb{Z}_n$ via the trace map

Dickson permutation polynomials that decompose in cycles of the same length

Equidistribution of roots of $L$-function of Gold exponential sum

The simplex code over Galois rings

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