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

摘要

In this article we construct an infinite family of linear error correcting codes over Fq for any prime power q. The code parameters are [q^2t + q^t−1 − q^2t−1 − q^t, 2t+1, q^2t + q^2t−2 + q^t−1 − 2q^2t−1 − q^t]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 = 2^t−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.