Optimal p-ary Codes from One-weight Linear Codes over Z_p^m

We investigate the structures and properties of one-Homogeneous (Lee) weight linear codes over the ring of integers modulo M (M is a power of a prime integer p) with one unique nonzero weight. We fully describe one-Homogeneous (Lee) weight codes over rings of integers modulo 4, 8 and 9. By the generalized Gray map, we obtain a class of optimal binary linear codes which reaches the Griesmer bound as well as the plotkin bound and a class of optimal p-ary (p is odd and prime) nonlinear codes which attains the Plotkin bound.