Key points are not available for this paper at this time.
Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer qᵏ-1q-1, k, q^k-1q-linear codes and they meet all Griesmer bounds of the generalized Hamming weights of linear codes. All the subcodes with dimension r of a qᵏ-1q-1, k, q^k-1q-simplex code have the same subcode support weight q^k-r (qʳ-1) q-1 for 1 r k. In this paper, we construct linear codes meeting the Griesmer bound of the r-generalized Hamming weight, such codes do not meet the Griesmer bound of the j-generalized Hamming weight for 1 j<r. Moreover these codes have only few subcode support weights. The weight distribution and the subcode support weight distributions of these distance-optimal codes are determined. Linear codes constructed in this paper are natural generalizations of distance-optimal few-weight codes.
Xu et al. (Mon,) studied this question.