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

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes978-3-642-02181-7Series ISSN 0302-9743 Series E-ISSN 1611-3349

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https://doi.org/10.1007/978-90-481-2383-4rithm, 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.

TSH582

https://doi.org/10.1007/978-90-481-2383-4s and properties as the codes in the usual binary linear Reed-Muller family have been introduced. A structural invariant, the rank, for binary codes is used to classify some of these ℤ.-linear codes. The rank is established generalizing the known results about the rank for ℤ.-linear Hadamard and ℤ.-linear extended 1-perfect codes.

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https://doi.org/10.1007/978-90-481-2383-4f the BIBD graphs and show that they yield optimal expander graphs that are also bipartite Ramanujan graphs. In particular, we show that the bipartite graphs derived from finite projective and affine geometries yield optimal Ramanujan graphs. This in turn leads to a theoretical explanation of the good performance of a class of LDPC codes.

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Sakib Bin Amin,Saanjaana Rahman.. 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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Lecture Notes in Computer Sciencehttp://image.papertrans.cn/a/image/159620.jpg

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An Extension of the Order Bound for AG Codesng-Rao bound. By using a finer partition of the set of all codewords of a code we improve the order bounds by Beelen and by Duursma and Park. We show that the new bound can be efficiently optimized and we include a numerical comparison of different bounds for all two-point codes with Goppa distance

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