2012/08/27 by Hajime Matsui, Matsui, Hajime
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.DM #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.1208.5429
6 pages, 2 columns, presented at The 34th Symposium on Information Theory and Its Applications (SITA2011)
arxiv created 2012/08/27 · openalex publication_date 2012/08/27 · arxiv updated 2012/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.