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TitleBounded distance decoding of linear error-correcting codes with Gröbner bases
Author(s) Stanislav Bulygin, Ruud Pellikaan
TypeArticle in Journal
AbstractThe 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.
KeywordsDecoding, Gröbner basis, Linear code, Minimum distance, Syndrome decoding, System of polynomial equations
URL http://www.sciencedirect.com/science/article/pii/S0747717108001776
JournalJournal of Symbolic Computation
Pages1626 - 1643
NoteGröbner Bases in Cryptography, Coding Theory, and Algebraic Combinatorics
Translation No
Refereed No