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 Fq2. From these geometric characterizations, we obtain explicit formulas. In particular, we determine the number of minimum-weight codewords for all Hermitian codes with d≤. q and all second-weight codewords for distance-3, 4 codes.

On the small weights codewords of some Hermitian codes

MARCOLLA, CHIARA;
2015-01-01

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 Fq2. From these geometric characterizations, we obtain explicit formulas. In particular, we determine the number of minimum-weight codewords for all Hermitian codes with d≤. q and all second-weight codewords for distance-3, 4 codes.
2015
73
27
45
Affine-variety code; Hamming weight; Hermitian code; Hermitian curve; Linear code; Minimum-weight words
Chiara Marcolla and Marco Pellegrini and Massimiliano Sala
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1525347
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