Details:
Title  On the Decoding of Cyclic Codes Using Gröbner Bases  Author(s)  Philippe Loustaunau, Eric V. York  Type  Article in Journal  Abstract  In this paper we revisit an algorithm presented by Chen, Reed, Helleseth, and Troung in [5] for decoding cyclic codes up to their true minimum distance using Gröbner basis techniques. We give a geometric characterization of the number of errors, and we analyze the corresponding algebraic characterization. We give a characterization for the error locator polynomial as well. We make these ideas effective using the theory of Gröbner bases. We then present an algorithm for computing the reduced Gröbner basis over ¶2 for the syndrome ideal of cyclic codes, with respect to a lexicographic term ordering. This algorithm does not use Buchberger's algorithm or the multivariable polynomial division algorithm, but instead uses the form of the generators of the syndrome ideal and an adaptation of the algorithm introduced in [11]. As an application of this algorithm, we present the reduced Gröbner basis for the syndrome ideal of the [23,r12,r7] Golay code, and a decoding algorithm.  Keywords  decoding, cyclic codes, Gröbner basis, zerodimensional ideals  Length  15  ISSN  09381279 
File 
 URL 
dx.doi.org/10.1007/s002000050084 
Language  English  Journal  Applicable Algebra in Engineering, Communication and Computing  Volume  8  Number  6  Pages  469483  Publisher  SpringerVerlag GmbH  Year  1997  Month  December  Translation 
No  Refereed 
No 
