A class of optimal p-ary codes from one-weight codes over Fp[u]/〈um〉

We characterize the structures and properties of one-homogeneous weight linear codes Ck1,…,km over Fp[u]/〈um〉 of type 1k1pk2⋯(pm−1)km with one unique nonzero weight w0. We introduce a distance-preserving Gray map from (Fp[u]/〈um〉)n to Fppm−1n. By the Gray map, we obtain a class of optimal p-ary one-Hamming weight linear codes from one-homogeneous weight linear codes over Fp[u]/〈um〉. We conclude by constructing some one-homogeneous codes over Fp[u]/〈um〉.