中文摘要：

利用Gray映射Φ的性质,研究了交换环=Fpk＋uFpk上任意长的循环码。其中p是素数,k是一给定的正整数。证明了环上长为n的码C是循环码当且仅当Φ（C）是Fpk上指标为pk长为npk的准循环码。特别地,环上长为n的线性循环码的Gray像是有限域Fpk上指标为pk长为npk的线性准循环码。

英文摘要：

Based on the property of Gray map Φ, studied cyclic codes of arbitrary length over the commutative ring R =F_ pk ＋uF_ pk , where p was a prime and k≥1 was a positive integer. Proved that a code C of length n over R was a cyclic code if and only if its Gray image was a quasi-cyclic code over F_ pk of index pk and length npk. In particular, the Gray image of a linear cyclic code of length n over R was a linear quasi-cyclic code over F_ pk of index pk and length npk.