OPTIMAL CODES OVER GF

Let nq(k; d) denote the smallest value of n for which there exists a linear [n; k; d]-code over GF(q). An [n; k; d]-code whose length is equal to nq(k; d) is called optimal. The problem of finding nq(k; d) has received much attention for the case q = 2. In this paper we present some matrix generators for the family of optimal [n; 3; d] and [n; 4; d] codes over GF(7).