设~$p$ 是一个奇素数且~$p\equiv 3$ (mod $4)$, $m$ 为奇数, $\alpha$为有 限域~${\mathbb{F}}_{p^m}$里面的一个本原元. 文章确定了有限域~${\mathbb{F}}_p$ 上具有 非零点~${\alpha }^{-1}$, ${\alpha }^{-l}$ 或~${\alpha }^{-1}$, ${\alpha }^{-t}$的循环码的重量分布,其中~$l,t$ 为满足某些条件的正整数. 结果推广了文献Ding等(2013) 及Zhou和Ding(2013) 的相应结果.

Let $p$ be an odd prime such that $p\equiv 3$ (mod $4)$, $m$ be odd, $\alpha$ be the primitive element of finite field ${\mathbb{F}}_{p^m}$. In this paper, the weight distribution of cyclic codes with nonzero ~${\alpha }^{-1}$, ${\alpha }^{-l}$ or~${\alpha }^{-1}$, ${\alpha }^{-t}$ are determined, where~$l,t$ are positive integers satisfied some conditions. The result generalizes the result in Ding, et al.(2013) and Zhou and Ding(2013).