Finite Fields And Applications: 7th International Conference, Fq7, Toulouse, France, May 5-9, 2003, Revised Papers (lecture Notes In Computer Science)

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. 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 - Thisvolumerepresentstherefereedproceedingsofthe7thInternationalC- ference on Finite Fields and Applications (F 7) held during May 5-9, q 2003, in Toulouse, France. The conference was hosted by the Pierre Baudis C- gress Center, downtown, and held at the excellent conference facility. This event continued a series of biennial international conferences on Finite Fields and - plications, following earlier meetings at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University of Glasgow (UK) in July 1995, the University of Waterloo (Canada) in August 1997, the Univ- sity of Augsburg (Germany) in August 1999, and the Universidad Aut ́ onoma Metropolitana-Iztapalapa, in Oaxaca (Mexico) in 2001. The Organizing Committee of F 7 consisted of Claude Carlet (INRIA, Paris, q France), Dieter Jungnickel (University of Augsburg, Germany), Gary Mullen (Pennsylvania State University, USA), Harald Niederreiter (National University of Singapore, Singapore), Alain Poli, Chair (Paul Sabatier University, Toulouse, France), Henning Stichtenoth (Essen University, Germany), and Horacio Tapia- Recillas (Universidad Aut ́ onoma Metropolitan-Iztapalapa, Mexico). The program of the conference consisted of four full days and one half day of sessions, with eight invited plenary talks, and close to 60 contributed talks Let (sn) be a q-periodic sequence over the residue class ring Zd.