A class of optimal pary codes from one-weight codes over F p 1⁄2

We characterize the structures and properties of one-homogeneous weight linear codes Ck1,...,km over Fp1⁄2u =/uS of type 11pk2 ðp 1Þm with one unique nonzero weight w0. We introduce a distance-preserving Gray map from ðFp1⁄2u =/umSÞ to F m n p . By the Gray map, we obtain a class of optimal p-ary one-Hamming weight linear codes from one-homogeneous weight linear codes over Fp1⁄2u =/uS. We conclude by constructing some one-homogeneous codes over Fp1⁄2u =/uS. & 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

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