Finite Fields and Applications: Proceedings of The Fifth International Conference on Finite Fields and Applications Fq 5, held at the University of Augsburg, Germany, August 2-6, 1999

by Dieter Jungnickel (Editor), H. Niederreiter (Editor)

Overview

The Fifth International Conference on Finite Fields and Applications Fq5 held at the University of Augsburg, Germany, from August 2-6, 1999 continued a series of biennial international conferences on finite fields. The proceedings document the steadily increasing interest in this topic. Finite fields have an inherently fascinating structure and are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields. This interplay has always been a dominant theme in Fq conferences and was very much in evidence at Fq5. The proceedings reflect this, and offer an up-to-date collection of surveys and original research articles by leading experts in the area.

Product Details

ISBN-13:	9783642624988
Publisher:	Springer Berlin Heidelberg
Publication date:	10/23/2012
Edition description:	Softcover reprint of the original 1st ed. 2001
Pages:	490
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Projective Generalized Reed-Muller Codes over p-adic Numbers and Finite Rings.- Towards a Basis for the Space of Regular Functions in a Tower of Function Fields Meeting the Drinfeld-Vladut Bound.- Self-Dual Normal Bases and Related Topics.- Permutations amongst the Dembowski-Ostrom Polynomials.- Associative Rational Functions in Two Variables.- A Note on the Minimal Polynomial of the Product of Linear Recurring Sequences.- Gelfond-Gramain’s Theorem for Function Fields.- On Generalized Bent and q-ary Perfect Nonlinear Functions.- Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group..- A Permutation of a Small Infinite Field.- Almost Perfect Nonlinear Power Functions on GF(2n): A New Case for n Divisible by 5.- On Non-Abelian Semi-Regular Relative Difference Sets.- Applications of Arithmetical Geometry to Cryptographic Constructions.- Gauß Periods in Finite Fields.- Constructions of Orthomorphisms of—2n.- Period Polynomials for $$ {F_{{{psub{2}}}}} $$ of Fixed Small Degree.- Universal Generators for Primary Closures of Galois Fields.- Irreducible Polynomials Generated by Decimations.- Decoding Reed-Muller Codes beyond Half the Minimum Distance.- On Binary Cyclic Codes With Few Weights.- Mac Williams Identities for Linear Codes over Finite Frobenius Rings.- Cyclotomic Function Fields with Many Rational Places.- On the Siamese Twin Designs.- On the Brauer Monoid for Finite Fields.- Algorithms for Factoring Polynomials over Finite Fields.- Gauss Sums over Quasi-Frobenius Rings.- On the Early History of Galois Fields.- Linear Blocking Sets: a Survey.- Comparison of Techniques on Divisibility Properties of Exponential Sums and Applications.- On the Rank of Appearance and the Number of Zeros of the Lucas Sequences over Fq.- APermutation Problem for Finite Fields.- The L-Function of Gold Exponential Sum.- On Permutation Polynomials and Derivable Translation Planes.- Pure L-Functions from Algebraic Geometry over Finite Fields.- Incomplete Additive Character Sums and Applications.- Applications of Algebraic Curves to Constructions of Codes and Almost Perfect Sequences.- Author Index.