跳频序列部分汉明相关理论界及其最优构造

Bounds on the Partial Hamming Correlaiton of Frequency-hopping Sequences and Their Optimal Constructions

具有优良部分汉明相关特性的跳频序列在通信和雷达中具有重要应用,与循环码、差族和差填充等数学对象具有紧密的联系.介绍跳频序列部分函数相关性的理论界及最优构造的研究现状,包括单条跳频序列的部分汉明相关理论界、跳频序列集的部分汉明相关性的下界、跳频序列集关于部分汉明相关的序列集大小的上界、具有最优序列集大小的严格最优部分汉明相关跳频序列集的新理论界,以及多类具有最优部分相关性质的跳频序列(集)的构造.

Frequency-hopping sequences(FHSs)with preferable partial Hamming correlation have important applications in communications and radar,which have close connections with many mathematical objects such as cyclic codes,difference families,and difference packings.The objective of this paper is to give a well-rounded survey of various lower bounds on partial Hamming correlation of FHSs and optimal constructions meeting the bounds.