Details:
Title  Use of Gröbner bases to decode binary cyclic codes up to the trueminimum distance  Author(s)  Xuemin Chen, Tor Helleseth, Irving S. Reed, TrieuKien Truong  Type  Article in Journal  Abstract  A general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t=[(d1)/2] errors, where d is the true minimum distance of the given cyclic code. The key idea behind this decoding technique is a systematic application of the algorithmic procedures of Grobner bases to obtain the errorlocator polynomial L(z). The discussion begins from a set of syndrome polynomials F and the ideal T(F) generated by F. It is proved here that the process of transforming F to the normalized reduced Grobner basis of I(F) with respect to the “purely lexicographical” ordering automatically converges to L(z). Furthermore, it is shown that L(z) can be derived from any normalized Grobner basis of I(F) with respect to any admissible total ordering. To illustrate this new approach, the procedures for decoding certain BCH codes and quadratic residue codes are demonstrated  ISSN  00189448 
Language  English  Journal  IEEE Transactions on Information Theory  Volume  40  Number  5  Year  1994  Month  September  Translation 
No  Refereed 
No 
