Efficient decoding of (binary) the correction capacity of the code using Gröbner bases
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Auteurs : Daniel Augot ; Magali Bardet ; Jean-Charles FaugèreSource :
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This paper revisits the topic of decoding cyclic codes with Gröbner bases. We introduce new algebraic systems, for which the Gröbner basis computation is easier. We show that formal decoding formulas are too huge to be useful, and that the most efficient technique seems to be to recompute a Gröbner basis for each word (online decoding). We use new Gröbner basis algorithms and ``trace preprocessing'' to gain in efficiency.
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