On the Gray images of some constacyclic codes over Fp+ u Fp+ u2Fp

摘要

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over Fp+ uFp+ u2Fpand codes over Fpis defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear (1+u+u2)-constacyclic code over Fp+ uFp+ u2Fpof length n is a repeated-root cyclic code over Fpof length pn. Furthermore, some examples of optimal linear cyclic codes over F3from (1 + u + u2)-constacyclic codes over F3 + uF3+ u2F3are given.

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