环Fp+uFp+vFp上的(1+u+v)-循环码

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。

(1+u+v)- cyclic codes over Fp+uFp+vFp

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] overFp]. And by this way, two optimal binary quasi-cyclic codes are constructed.