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.
Author(s): Wilfried Meidl, Arne Winterhof (auth.), Gary L. Mullen, Alain Poli, Henning Stichtenoth (eds.)
Series: Lecture Notes in Computer Science 2948
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2004
Language: English
Pages: 263
Tags: Numeric Computing; Coding and Information Theory; Algorithm Analysis and Problem Complexity; Symbolic and Algebraic Manipulation; Field Theory and Polynomials; Computational Science and Engineering
Front Matter....Pages -
On the Autocorrelation of Cyclotomic Generators....Pages 1-11
The Weierstrass Semigroup of an m -tuple of Collinear Points on a Hermitian Curve....Pages 12-24
On Cyclic Top-Associative Generalized Galois Rings....Pages 25-39
Linear Recurrences with Polynomial Coefficients and Computation of the Cartier-Manin Operator on Hyperelliptic Curves....Pages 40-58
Mutual Irreducibility of Certain Polynomials....Pages 59-68
Lattice Profile and Linear Complexity Profile of Pseudorandom Number Sequences....Pages 69-78
Symplectic Spreads and Permutation Polynomials....Pages 79-88
What Do Random Polynomials over Finite Fields Look Like?....Pages 89-108
Combinatorics of the Two-Variable Zeta Function....Pages 109-136
Constructions of Mutually Unbiased Bases....Pages 137-144
A Construction of Matrices with No Singular Square Submatrices....Pages 145-147
Everywhere Ramified Towers of Global Function Fields....Pages 148-153
On the Construction of Some Towers over Finite Fields....Pages 154-165
The Covering Radius of Some Primitive Ternary BCH Codes....Pages 166-180
The Gray Map on GR( p 2 , n ) and Repeated-Root Cyclic Codes....Pages 181-196
Primitive Polynomials over Small Fields....Pages 197-214
Vectorial Functions and Covering Sequences....Pages 215-248
u q -Sharp Subsets of a Finite Field....Pages 249-253
Cyclic Decomposition of Permutations of Finite Fields Obtained Using Monomials....Pages 254-261
Back Matter....Pages -
