关于素数幂$p^m(m>1)$, 首先给出了一类新的广义分圆及其性质; 其次, 基于此广义分圆法构造了一类周期为$p^m$的跳频序列族; 最后证明了该序列族关于平均汉明相关界是最优的, 而且当$m=2$时该序列族关于最大汉明相关界也是最优的.

Firstly, a kind of generalized cyclotomy with respect to a prime-power $p^m(m>1)$ is presented and its properties are investigated; Secondly, based upon the generalized cyclotomy, a class of frequency-hopping sequences (FHSs) set with length of sequences being $p^m$ is constructed; Finally, it is proved that the proposed FHSs set is not only optimal with regard to the average Hamming correlation (AHC) bound, but also optimal with regard to the maximal Hamming correlation (MHC) bound when $m=2$.