Fast Erasure-and-Error Decoding and Systematic Encoding of a Class of Affine Variety Codes release_csnxwvgyj5frrawwppiuagt3me

by Hajime Matsui

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In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector spaces, one corresponds to information symbols and the other is indexed by the support of Grobner basis, are canonically isomorphic, and moreover, the isomorphism is given by the extension through linear feedback shift registers from Grobner basis and discrete Fourier transforms. Next, the lemma is applied to fast unified system of encoding and decoding erasures and errors in a certain class of affine variety codes.
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Type  article
Stage   submitted
Date   2012-08-27
Version   v1
Language   en ?
arXiv  1208.5429v1
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