Frequency-hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency-hopping spread spectrum systems. In this paper, we present two new constructions for FHS sets. We first give a new construction for FHS sets of length nN for two positive integers n and N with gcd (n,N)=1. We then present another construction for FHS sets of length (q-1)N , where q is a prime power satisfying gcd (q-1,N)=1. By these two constructions, we obtain infinitely many new optimal FHS sets with respect to the Peng-Fan bound as well as new optimal FHSs with respect to the Lempel-Greenberger bound, which have length $nN$ or n(q-1)N. As a result, a great deal of flexibility may be provided in the choice of FHS sets for a given frequency-hopping spread spectrum system.
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机译：跳频序列（FHS）用于缓解由跳频扩频系统中的频率冲击引起的干扰。在本文中，我们介绍了FHS装置的两种新结构。我们首先为gcd（n，N）= 1的两个正整数n和N给出长度为NN的FHS集的新构造。然后，我们为长度为（q-1）N的FHS集提出另一种构造，其中q是满足gcd（q-1，N）= 1的素数幂。通过这两种构造，我们获得了关于Peng-Fan界的无限多个新的最优FHS集以及关于Lempel-Greenberger界的新最优FHS，其长度为$ nN $或n（q-1）N 。结果，对于给定的跳频扩频系统，在选择FHS集时可以提供很大的灵活性。
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