On the small-weight codewords of some Hermitian codes. (March 2016)

• Record Type: Journal Article
• Authors: Marcolla, Chiara; Pellegrini, Marco; Sala, Massimiliano
• Is Part Of: Journal of symbolic computation. Volume 73(2016)
• Page Start: 27
• Page End: 45
• Publication Date: 2016-03
• Subjects: Affine-variety code -- Hamming weight -- Hermitian code -- Hermitian curve -- Linear code -- Minimum-weight words; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.03.003
• Languages: English
• ISSNs: 0747-7171

Abstract

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.