On the small-weight codewords of some Hermitian codes. (March 2016) - Marcolla, Chiara; Pellegrini, Marco; Sala, Massimiliano
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.