Construction of cubic self-dual codes

We present a building-up construction method for quasi-cyclic self-dual codes over finite fields. By using this, we give cubic (i.e., lscr-quasi-cyclic codes of length 3lscr) 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.