Experimental constructions of self-dual codes

Abstract

We give a general experimental method generalizing the codes of Carlach and Vervoux (Proceedings of the 13th Applicable Algebra in Engineering Communication and Computing (AAECC 13), Hawaii, USA, 14–19 November 1999, p. 15) to construct self-dual codes. We consider the particular fields GF(2), GF(3), GF(4) (both Euclidean and Hermitian cases), GF(5) and GF(7). We give numerical tables of the best known self-dual codes over these alphabets up to lengths where minimum distances are computable. These tables regularly fill gaps between known codes with good parameters such as the quadratic residue codes, the Pless symmetry codes (J. Combin. Theory Ser. A A12 (1972) 119) or the quadratic double circulant codes (J. Combin. Theory Ser. A 97 (2002) 85). Many new codes with better parameters are constructed: in particular the first extremal ternary self-dual [52,26,15] and [78,39,18] codes and the first binary self-dual [114,57,18] and [116,58,18] codes are constructed. We also give the minimum weight of the Pless symmetry codes of length 84. We also update tables for quadratic residue codes over GF(4), GF(5) and GF(7) and we obtain in particular a [62,31,20] code over GF(5).