Finite Fields and Applications 7th International Conference, Fq7, Toulouse, France, May 5-9, 2003, Revised Papers

This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004.
The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.

On the Autocorrelation of Cyclotomic Generators.- The Weierstrass Semigroup of an m-tuple of Collinear Points on a Hermitian Curve.- On Cyclic Top-Associative Generalized Galois Rings.- Linear Recurrences with Polynomial Coefficients and Computation of the Cartier-Manin Operator on Hyperelliptic Curves.- Mutual Irreducibility of Certain Polynomials.- Lattice Profile and Linear Complexity Profile of Pseudorandom Number Sequences.- Symplectic Spreads and Permutation Polynomials.- What Do Random Polynomials over Finite Fields Look Like?.- Combinatorics of the Two-Variable Zeta Function.- Constructions of Mutually Unbiased Bases.- A Construction of Matrices with No Singular Square Submatrices.- Everywhere Ramified Towers of Global Function Fields.- On the Construction of Some Towers over Finite Fields.- The Covering Radius of Some Primitive Ternary BCH Codes.- The Gray Map on GR(p 2, n) and Repeated-Root Cyclic Codes.- Primitive Polynomials over Small Fields.- Vectorial Functions and Covering Sequences.- u q -Sharp Subsets of a Finite Field.- Cyclic Decomposition of Permutations of Finite Fields Obtained Using Monomials.