Details:
Title  Improved decoding of affinevariety codes  Author(s)  Chiara Marcolla, Emmanuela Orsini, Massimiliano Sala  Type  Article in Journal  Abstract  General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for a large class of linear codes. We provide some decoding techniques for affinevariety codes using some multidimensional extensions of general error locator polynomials. We prove the existence of such polynomials for any correctable affinevariety code and hence for any linear code. We propose two main different approaches, that depend on the underlying geometry. We compute some interesting cases, including Hermitian codes. To prove our coding theory results, we develop a theory for special classes of zerodimensional ideals, that can be considered generalizations of stratified ideals. Our improvement with respect to stratified ideals is twofold: we generalize from one variable to many variables and we introduce points with multiplicities.  ISSN  00224049 
URL 
http://www.sciencedirect.com/science/article/pii/S0022404912000114 
Language  English  Journal  Journal of Pure and Applied Algebra  Volume  216  Number  7  Pages  1533  1565  Year  2012  Edition  0  Translation 
No  Refereed 
No 
