Titlebook: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes; 18th International S Maria Bras-Amorós,Tom Høholdt Conference proceedings

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There Are Not Non-obvious Cyclic Affine-invariant CodesWe show that an affine-invariant code . of length .. is not permutation equivalent to a cyclic code except in the obvious cases: . = 1 or . is either {0}, the repetition code or its dual.

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Noisy Interpolation of Multivariate Sparse Polynomials in Finite FieldsWe consider the problem of recovering an unknown sparse multivariate polynomial . over a finite field . of prime order . from approximate values of .(..,...,..) at polynomially many points . selected uniformly at random. Our result is based on a combination of bounds on exponential sums with the lattice reduction technique.

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From the Euclidean Algorithm for Solving a Key Equation for Dual Reed–Solomon Codes to the Berlekamprithm, both designed to solve a key equation. This article presents a new version of the key equation and a way to use the Euclidean algorithm to solve it. A straightforward reorganization of the algorithm yields the Berlekamp-Massey algorithm.

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On Self-dual Codes over ,,.. and give a necessary and sufficient condition for the self-duality of induced codes. We then give an inductive algorithm for constructing all self-dual codes over .., and establish the mass formula, which counts the number of such codes.

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978-3-642-02180-0Springer-Verlag Berlin Heidelberg 2009

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