Few-weight codes over F_p+u F_p associated with down sets and their distance optimal Gray image

10/17/2019

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by   Yansheng Wu, et al.

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Let p be an odd prime number. In this paper, we construct 2(2p-3) classes of codes over the ring R= F_p+u F_p,u^2=0, which are associated with down-sets. We compute the Lee weight distributions of the 2(2p-3) classes of codes when the down-sets are generated by a single maximal element. Moreover, by using the Gray map of the linear codes over R, we find out 2(p-1) classes of p-ary distance optimal linear codes. Two classes of them are attained the Griesmer bound with equality as well.