For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We are able to obtain geometric characterizations for small-weight codewords for some families of Hermitian codes over any F_{q^2}. From these geometric characterizations, we obtain explicit formulas. In particular, we determine the number of minimum-weight codewords for all Hermitian codes with d
On the small-weight codewords of some Hermitian codes / Marcolla, Chiara; Pellegrini, Marco; Sala, Massimiliano. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 73:(2016), pp. 27-45. [10.1016/j.jsc.2015.03.003]
On the small-weight codewords of some Hermitian codes
Marcolla, Chiara;Sala, Massimiliano
2016-01-01
Abstract
For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We are able to obtain geometric characterizations for small-weight codewords for some families of Hermitian codes over any F_{q^2}. From these geometric characterizations, we obtain explicit formulas. In particular, we determine the number of minimum-weight codewords for all Hermitian codes with d| File | Dimensione | Formato | |
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Descrizione: On the small weights codewords of some Hermitian codes
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