Efficient decoding of (binary) the correction capacity of the code using Gröbner bases
Identifieur interne : 003A07 ( Crin/Curation ); précédent : 003A06; suivant : 003A08Efficient decoding of (binary) the correction capacity of the code using Gröbner bases
Auteurs : Daniel Augot ; Magali Bardet ; Jean-Charles FaugèreSource :
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Abstract
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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<author><name sortKey="Augot, Daniel" sort="Augot, Daniel" uniqKey="Augot D" first="Daniel" last="Augot">Daniel Augot</name>
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<author><name sortKey="Bardet, Magali" sort="Bardet, Magali" uniqKey="Bardet M" first="Magali" last="Bardet">Magali Bardet</name>
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<author><name sortKey="Faugere, Jean Charles" sort="Faugere, Jean Charles" uniqKey="Faugere J" first="Jean-Charles" last="Faugère">Jean-Charles Faugère</name>
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<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>cyclic codes</term>
<term>decoding</term>
<term>error-locator polynomial</term>
<term>gröbner bases</term>
<term>ideal theory</term>
<term>newton identities</term>
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<front><div type="abstract" xml:lang="en" wicri:score="619">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.</div>
</front>
</TEI>
<BibTex type="inproceedings"><ref>augot03a</ref>
<crinnumber>A03-R-276</crinnumber>
<category>3</category>
<equipe>CODES</equipe>
<author><e>Augot, Daniel</e>
<e>Bardet, Magali</e>
<e>Faugère, Jean-Charles</e>
</author>
<title>Efficient decoding of (binary) the correction capacity of the code using Gröbner bases</title>
<booktitle>{IEEE International Symposium on Information Theory 2003 - ISIT'2003, Yokohama, Japon}</booktitle>
<year>2003</year>
<month>Jul</month>
<publisher>IEEE</publisher>
<keywords><e>decoding</e>
<e>cyclic codes</e>
<e>ideal theory</e>
<e>gröbner bases</e>
<e>error-locator polynomial</e>
<e>newton identities</e>
</keywords>
<abstract>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.</abstract>
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