Paper Info
Title
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 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.
Year
Venue
Field
2012
CoRR
Discrete mathematics,Sequential decoding,Algebra,Affine variety,Block code,Coding theory,Linear code,Gröbner basis,List decoding,Lemma (mathematics),Mathematics
DocType
Volume
Citations 
Journal
abs/1208.5429
1
PageRank 
References 
Authors
0.35
6
1
Name
Order
Citations
PageRank
Hajime Matsui1188.14