Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings

Jacques Stern (auth.), Marc Fossorier, Tom Høholdt, Alain Poli (eds.)3540401113, 9783540401117

This book constitutes the refereed proceedings of the 15th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-15, held in Toulouse, France, in May 2003.

The 25 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 40 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.

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Table of contents :
Cryptography and the Methodology of Provable Security….Pages 1-5
Dynamical Systems Generated by Rational Functions….Pages 6-17
Homotopy Methods for Equations over Finite Fields….Pages 18-23
Three Constructions of Authentication/Secrecy Codes….Pages 24-33
The Jacobi Model of an Elliptic Curve and Side-Channel Analysis….Pages 34-42
Fast Point Multiplication on Elliptic Curves through Isogenies….Pages 43-50
Interpolation of the Elliptic Curve Diffie-Hellman Mapping….Pages 51-60
An Optimized Algebraic Method for Higher Order Differential Attack….Pages 61-70
Fighting Two Pirates….Pages 71-78
Copyright Control and Separating Systems….Pages 79-86
Unconditionally Secure Homomorphic Pre-distributed Commitments….Pages 87-97
A Class of Low-Density Parity-Check Codes Constructed Based on Reed-Solomon Codes with Two Information Symbols….Pages 98-107
Relative Duality in MacWilliams Identity….Pages 108-118
Good Expander Graphs and Expander Codes: Parameters and Decoding….Pages 119-128
On the Covering Radius of Certain Cyclic Codes….Pages 129-138
Unitary Error Bases: Constructions, Equivalence, and Applications….Pages 139-149
Differentially 2-Uniform Cocycles — The Binary Case….Pages 150-157
The Second and Third Generalized Hamming Weights of Algebraic Geometry Codes….Pages 158-168
Error Correcting Codes over Algebraic Surfaces….Pages 169-179
A Geometric View of Decoding AG Codes….Pages 180-190
Performance Analysis of M-PSK Signal Constellations in Riemannian Varieties….Pages 191-203
Improvements to Evaluation Codes and New Characterizations of Arf Semigroups….Pages 204-215
Optimal 2-Dimensional 3-Dispersion Lattices….Pages 216-225
On g -th MDS Codes and Matroids….Pages 226-234
On the Minimum Distance of Some Families of ℤ 2 k -Linear Codes….Pages 235-243
Quasicyclic Codes of Index ℓ over F q Viewed as F q [ x ]-Submodules of F q ℓ [ x ]/〈 x m −1〉….Pages 244-253
Fast Decomposition of Polynomials with Known Galois Group….Pages 254-264