The study of aperiodic Hamming correlation (APC) of frequency hopping sequences (FHSs) is a hard problem that has not been paid enough attention in the literature. For low-hit-zone (LHZ) FHSs, the study of APC becomes more difficult. We call them LHZ FHSs under APC (LHZ-APC FHSs). LHZ-APC FHSs are studied for the first time in this paper. First, we establish a bound on the family sizes of LHZ-APC FHS sets. Then we present a method for constructions of LHZ-APC FHS sets based on conventional FHS sets under periodic Hamming correlation (conventional PC FHS sets). By choosing different conventional PC FHS sets, we obtain three classes of LHZ-APC FHS sets whose family sizes are optimal or near optimal according to this new bound. Further, we modify the construction method and get more new LHZ-APC FHS sets with optimal family sizes.

跳频序列（FHS）的非周期汉明相关（APC）的研究是一个难题，在文献中尚未引起足够的重视。对于低命中区（LHZ）FHS，APC 的研究变得更加困难。我们将它们称为 APC 下的 LHZ FHS (LHZ-APC FHS)。本文首次研究了LHZ-APC FHS。首先，我们对 LHZ-APC FHS 集的家族规模建立了界限。然后我们提出了一种基于周期性汉明相关下的传统FHS集（传统PC FHS集）构造LHZ-APC FHS集的方法。通过选择不同的传统PC FHS集，我们获得了三类LHZ-APC FHS集，根据这个新界限，它们的家族规模是最优的或接近最优的。进一步，我们修改了构造方法，得到了更多具有最佳族规模的新LHZ-APC FHS集。