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On the weights of affine-variety codes and some Hermitian codes

Marco Pellegrini 1 Chiara Marcolla 2 Massimiliano Sala 2 
1 Dipartimento di Informatica [Pisa]
2 Department of mathematics/Dipartimento di Matematica [Univ. Trento]
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.
Keywords : Affine-variety codes linear code distance minimum-weight word Hermitian code
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Submitted on : Wednesday, August 10, 2011 - 2:24:09 PM
Last modification on : Saturday, June 8, 2019 - 2:14:02 PM
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  • HAL Id : inria-00614257, version 1

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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. ⟨inria-00614257⟩

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