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 xed-point-free and xed-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.

Keywords: Self-orthogonal code, Bush-type Hadamard matrix, symmetric design

Quaestiones Mathematicae 36(2013), 341-352