For any ane-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.
On the weights of affine-variety codes and some Hermitian codes
Sala, Massimiliano;Marcolla, Chiara;
2011-01-01
Abstract
For any ane-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.File in questo prodotto:
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