A characterization of some {3vμ + 1, 3vμ; k - 1, q}-minihypers and some [n, k, qk-1 - 3qμ; q]-codes (k ⩾ 3, q ⩾ 5, 1 ⩽ μ < k - 1) meeting the Griesmer bound Original Research Article

For any [n, k, d; q]-code the Griesmer bound says that n ⩾∑i=0k−1⌈dqi⌉. The purpose of this paper is to characterize all [n, k, qk-1 - 3qμ; q]-codes meeting the Griesmer bound in the case where k ⩾ 3, q ⩾ 5 and 1 ⩽ μ < k - 1. It is shown that all such codes have a generator matrix whose columns correspond to all points in PG(k - 1, q) except for the points in a disjoint union of three μ-flats in PG(k - 1, q).