关键词: [(1+u+v)-]循环码, Gray映射, 准循环码

Abstract: Constacyclic codes are an important class of linear codes in coding theory. This class of codes has been widely used in practice because its error-correcting performance is easy to be analyzed. Meanwhile, many optimal linear codes are produced directly from constacyclic codes over finite rings. Firstly, the concept of [(1+u+v)-]cyclic code over [Fp+uFp+vFp]is defined, and the generator polynomial of [(1+u+v)-]cyclic codes is discussed. Then, a new Gray map [?] from [Fp+uFp+][vFp] to [F2pp] is introduced. It is proved that the Gray image of a [(1+u+v)-]cyclic code of length [n] over [Fp+uFp+vFp] is a linear quasi-cyclic code of index 2 and of length [2pn] over[Fp]. And by this way, two optimal binary quasi-cyclic codes are constructed.

Key words: (1+u+v)-cyclic code, Gray map, quasi-cyclic code