A class of optimal p-ary codes from one-weight codes over

We characterize the structures and properties of one-homogeneous weight linear codes C k 1 , … , k m over F p [ u ] / 〈 u m 〉 of type 1 k 1 p k 2 ⋯ ( p m − 1 ) k m with one unique nonzero weight w0. We introduce a distance-preserving Gray map from ( F p [ u ] / 〈 u m 〉 ) n to F p p m − 1 n . By the Gray map, we obtain a class of optimal p-ary one-Hamming weight linear codes from one-homogeneous weight linear codes over F p [ u ] / 〈 u m 〉 . We conclude by constructing some one-homogeneous codes over F p [ u ] / 〈 u m 〉 .