科研之友
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摘要
We devote to studying one?weight ZpZp[u]?additive codes, where p is an odd prime number. We derive a MacWilliams?type identity that relates the weight enumerators of a ZpZp[u]?additive code with its dual, and obtain a lower bound for the minimum distance of dual codes of one?weight additive codes. Some structural properties of one?weight ZpZp[u]?additive codes are considered. By the Gray map, we obtain a family of optimal one?Hamming weight p?ary codes from one?weight ZpZp[u]?additive codes, which attain the Plotkin bound and Griesmer bound. Additionally, we describe some constructions of one?weight ZpZp[u]?additive codes.
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