Abstract : For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We use our ideal and a geometric characterization to determine the number of small-weight codewords for some families of Hermitian codes over any Fq. In particular, we determine the number of minimum-weight code- words for all Hermitian codes with d ≤ q. For such codes we also count some other small-weight codewords.
https://hal.inria.fr/inria-00614257
Contributeur : Marie Trape
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Soumis le : mercredi 10 août 2011 - 14:24:09
Dernière modification le : mercredi 29 novembre 2017 - 10:26:41
Document(s) archivé(s) le : lundi 12 novembre 2012 - 15:16:38
Marco Pellegrini, Chiara Marcolla, Massimiliano Sala. On the weights of affine-variety codes and some Hermitian codes. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.273-282, 2011. 〈inria-00614257〉
