Efficient decoding of (binary) cyclic codes above the correction capacity of the code using Grobner bases
Résumé
This paper revisits the topic of decoding cyclic codes with Grobner bases. We introduce. new algebraic systems, for which the Grobner basis com- putation is easier. We show that formal decoding for- mulas are too huge to be useful, and that the most ef- ficient technique seems to be to recompute a Grobner basis for each word (online decoding). We use new Grobner basis algorithms and “trace preprocessing” to gain in efficiency.
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