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In literatures, there are various constructions of frequency hopping sequence(FHS for short) sets with good Hamming correlations. Some papers employed onlymultiplicative groups of finite fields to construct FHS sets, while otherpapers implicitly used only additive groups of finite fields for constructionof FHS sets. In this paper, we make use of both multiplicative and additivegroups of finite fields simultaneously to present a construction of optimal FHSsets. The construction provides a new family of optimal$\left(q^m-1,\frac{q^{m-t}-1}{r},rq^t;\frac{q^{m-t}-1}{r}+1\right)$ frequencyhopping sequence sets archiving the Peng-Fan bound. Thus, the FHS setsconstructed in literatures using either multiplicative groups or additivegroups of finite fields are all included in our family. In addition, some otherFHS sets can be obtained via the well-known recursive constructions throughone-coincidence sequence set.

A Construction of Optimal Frequency Hopping Sequence Set via Combination of Multiplicative and Additive Groups of Finite Fields