On the minimum length of q-ary linear codes of dimension four Original Research Article

Values and lower bounds for nq(4,d) for general q are given, where nq(k,d) denotes the minimum integer n for which there exists a linear code of length n, dimension k and minimum Hamming distance d over the Galois field GF(q). As a result for the nonprojective linear codes, we prove the nonexistence of an [n,4,2q3−rq2−q+1]q code attaining the Griesmer bound for q>r, r=3,4, and for q>2(r−1), r⩾3.