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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

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Table of Contents

Cryptography and the Methodology of Provable Security.- Dynamical Systems Generated by Rational Functions.- Homotopy Methods for Equations over Finite Fields.- Three Constructions of Authentication/Secrecy Codes.- The Jacobi Model of an Elliptic Curve and Side-Channel Analysis.- Fast Point Multiplication on Elliptic Curves through Isogenies.- Interpolation of the Elliptic Curve Diffie-Hellman Mapping.- An Optimized Algebraic Method for Higher Order Differential Attack.- Fighting Two Pirates.- Copyright Control and Separating Systems.- Unconditionally Secure Homomorphic Pre-distributed Commitments.- A Class of Low-Density Parity-Check Codes Constructed Based on Reed-Solomon Codes with Two Information Symbols.- Relative Duality in MacWilliams Identity.- Good Expander Graphs and Expander Codes: Parameters and Decoding.- On the Covering Radius of Certain Cyclic Codes.- Unitary Error Bases: Constructions, Equivalence, and Applications.- Differentially 2-Uniform Cocycles - The Binary Case.- The Second and Third Generalized Hamming Weights of Algebraic Geometry Codes.- Error Correcting Codes over Algebraic Surfaces.- A Geometric View of Decoding AG Codes.- Performance Analysis of M-PSK Signal Constellations in Riemannian Varieties.- Improvements to Evaluation Codes and New Characterizations of Arf Semigroups.- Optimal 2-Dimensional 3-Dispersion Lattices.- On g-th MDS Codes and Matroids.- On the Minimum Distance of Some Families of ?2 k-Linear Codes.- Quasicyclic Codes of Index ? over F q Viewed as F q[x]-Submodules of F q ?[x]/?x m?1?.- Fast Decomposition of Polynomials with Known Galois Group.

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