基于分圆理论和中国剩余定理的最优平均汉明相关跳频序列集构造

在跳频通信系统中，跳频序列的性能对整个跳频通信系统有着决定性的影响。设计出满足理论界要求的跳频序列集是研究跳频通信系统的关键内容。平均汉明相关值是衡量跳频序列性能优劣的重要指标。文章首先根据环上分圆的性质选取基序列，然后基于分圆理论和中国剩余定理，扩展序列构造了一类具有灵活参数的跳频序列集，并证明了所得到的跳频序列集关于平均汉明相关理论界最优。

Construction of Frequency-Hopping Sequence Sets with Optimal Average Hamming Correlation Based on Cyclotomy and Chinese Remainder Theorem

In frequency hopping communication system, frequency hopping sequences have a decisive influence on the entire frequency hopping communication system. Constructing a set of frequency hopping sequences that meet the requirements of the theoretical bound is the key content of researching frequency hopping communication systems. The average Hamming correlation is used to measure the average error of the frequency hopping communication system. In this paper, we first choose a basis sequence based on cyclotomy and then a set of frequency hopping sequences is constructed based on cyclotomy and the Chinese remainder theorem in the finite field. The results show that the proposed set with more flexible parameters is optimal with respect to the average Hamming correlation.