Self-dual codes over ℤ4 and unimodular lattices using orthogonal designs

Abstract

Hadamard matrices and weighing matrices have been used widely in the construction of binary and ternary self-dual codes. Recently orthogonal designs have been used to construct some new extremal self-dual codes over larger fields such as GF(5) and GF(7) as well as Type II self-dual codes over Z_2k, k = 2, 3, . . . , 11. In this paper we use orthogonal designs of order 12, to construct self-dual (Type II and Type I) codes over Z₄ of length 24 and then even unimodular lattices.