Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices

Abstract

In this article we construct an infinite family of linear error correcting codes over Fq for any prime power q. The code parameters are [q2t + qt-1 - q2t-1 - qt, 2t+1, q2t + q2t-2 + qt-1 - 2q2t-1 - qt]q, for any positive integer t. This family is a generalisation of the optimal self-complementary binary codes with parameters [2u2 - u, 2t + 1, u2 - u]2, where u = 2t-1. The codes are obtained by considering a submatrix of a specially constructed generalised Hadamard matrix. The optimality of the family is confirmed by using a recently derived generalisation of the Grey-Rankin bound when t >; 1, and the Griesmer bound when t = 1.