Self-orthogonal codes from some Bush-type Hadamard matrices

Abstract

By means of a construction method outlined by Harada and Tonchev, we determine some non-binary self-orthogonal codes obtained from the row span of orbit matrices of Bush-type Hadamard matrices that admit a fixed-point-free and fixed-block-free automorphism of prime order. We show that the code [20, 15, 4]5 obtained from a (100, 45, 20) design is optimal, and those with parameters [36, 21, 6]3 and [20, 14, 4]5 obtained from a (36, 15, 6) and a (100, 45, 20) design respectively, are near-optimal for the given length and dimension. Furthermore, we obtained a conjecturally optimal self-dual doubly-even [72, 36, 12]2 code, and examined the code of an orbit matrix of a putative (676, 325, 156) design.