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

Abstract

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 Gröbner basis, are canonically… (More)

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