Optimal ternary linear codes

Let n_q(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 n_q(k, d) is called optimal. The problem of finding n_q(k, d)has received much attention for the case q = 2. We generalize several results to the case of an arbitrary prime power q as well as introducing new results and a detailed methodology to enable the problem to be tackled over any finite field.In particular, we study the problem with q = 3 and determine n₃(k, d) for all d when k 4, and n₃(5, d) for all but 30 values of d.