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

In this article we construct an infinite family of linear error correcting codes over F q 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.