1. On the small-weight codewords of some Hermitian codes.
- Author
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Marcolla, Chiara, Pellegrini, Marco, and Sala, Massimiliano
- Subjects
- *
HERMITIAN forms , *INFORMATION storage & retrieval systems -- Code words , *MATHEMATICAL formulas , *LINEAR codes , *MATHEMATICAL analysis - 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 ≤ q and all second-weight codewords for distance- 3 , 4 codes. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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