Abstract
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
[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
[2(u2) - u, 2t + 1, u(2) - 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.