Efficient decoding of (binary) cyclic codes above the correction capacity of the code using Grobner bases

Daniel Augot 1 Magali Bardet 2, 3 Jean-Charles Faugère 4, 3
1 CODES - Coding and cryptography
Inria Paris-Rocquencourt
3 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
4 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : 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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Daniel Augot, Magali Bardet, Jean-Charles Faugère. Efficient decoding of (binary) cyclic codes above the correction capacity of the code using Grobner bases. IEEE International Symposium on Information Theory - ISIT'2003, Jun 2003, Yokohama, Japan. pp.362 - 362, ⟨10.1109/ISIT.2003.1228378⟩. ⟨inria-00509269⟩

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