Frequency-hopping sequences (FHSs) with favorite partial Hamming correlation properties are intensively needed in many synchronization and multiple-access systems. Strictly optimal FHS sets are a kind of FHS sets which has optimal Hamming correlation for any correlation window. In this paper, firstly we present simplified representations of the generalized Lempel–Greenberger bound on the partial Hamming autocorrelation of an FHS and the generalized Peng-Fan bound on the partial Hamming correlation of an FHS set, respectively. Secondly, we propose a direct construction of strictly optimal FHS sets, which interprets the previous construction proposed by Cai, Zhou, Yang and Tang. By choosing appropriate parameters and bijections, we present more flexible constructions of strictly optimal FHS sets.

中文翻译：

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FHS集的简化界及其严格优化构造

在许多同步和多址系统中，迫切需要具有最喜欢的部分汉明相关特性的跳频序列 (FHS)。严格最优 FHS 集是一种对任何相关窗都具有最优汉明相关性的 FHS 集。在本文中，我们首先分别给出了 FHS 的部分汉明自相关上的广义 Lempel-Greenberger 界和 FHS 集的部分汉明相关的广义 Peng-Fan 界的简化表示。其次，我们提出了严格最优 FHS 集的直接构造，它解释了 Cai、Zhou、Yang 和 Tang 提出的先前构造。通过选择适当的参数和双射，我们提出了更灵活的严格最优 FHS 集的构造。