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

摘要： 常循环码是一类重要的线性码，由于其纠错性能易于分析，因而广泛应用于实践中，同时，利用有限环上常循环码还可以直接构造最优线性码。定义了有限非链环[Fp+uFp+vFp]上[(1+u+v)]-循环码的相关概念，讨论了其生成多项式；引入了一种新的Gray映射[?]，证明了该环上[(1+u+v)]-循环码在此Gray映射[?]下的[p]元象是一个长为[2pn]的2-准循环码，并由此构造出了两个最优二元准循环码。

关键词: [(1+u+v)-]循环码, Gray映射, 准循环码