In this paper we consider all self-orthogonal [n, 1/2(n-1)] codes for n odd and 3 n 19, all self-dual [n, 1/2n] codes for n even and 2 n 24 and some other codes over GF(2) and answer to a question which of them have efficient coordinate ordering. As a result the exact values of their state complexities are determined. Sufficient conditions for codes to have an efficient coordinate ordering are derived also.