Details:
Title  Bounded distance decoding of linear errorcorrecting codes with Gröbner bases  Author(s)  Stanislav Bulygin, Ruud Pellikaan  Type  Article in Journal  Abstract  The problem of bounded distance decoding of arbitrary linear codes using Gröbner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving a certain system of polynomial equations over a finite field. The peculiarity of this system is that, when we want to decode up to half the minimum distance, it has a unique solution even over the algebraic closure of the considered finite field, although field equations are not added. The equations in the system have degree at most 2. As our experiments suggest, our method is much faster than the one of Fitzgerald–Lax. It is also shown via experiments that the proposed approach in some range of parameters is superior to the generic syndrome decoding.  Keywords  Decoding, Gröbner basis, Linear code, Minimum distance, Syndrome decoding, System of polynomial equations  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108001776 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  12  Pages  1626  1643  Year  2009  Note  Gröbner Bases in Cryptography, Coding Theory, and Algebraic Combinatorics  Edition  0  Translation 
No  Refereed 
No 
