Construction of cubic self-dual codes

Abstract

We present a building-up construction method for quasi-cyclic self-dual codes over finite fields. By using this, we give cubic (i.e., ℓ-quasi-cyclic codes of length 3ℓ) self-dual codes over various finite fields, which are optimal or have the best known parameters. In particular, we find a new quasi-cyclic self-dual [24; 12; 9] code over F5, whose corresponding lattice by Construction A is shown to be the odd Leech lattice O24. Only one self-dual [24; 12; 9] code over F5 was known before up to monomial equivalence. © 2009 IEEE.