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In this paper, a new class of frequency hopping sequences (FHSs) of length $p^{n} $ is constructed by using Ding-Helleseth generalized cyclotomic classesof order 2, of which the Hamming auto- and cross-correlation functions areinvestigated (for the Hamming cross-correlation, only the case $ p\equiv 3\pmod4 $ is considered). It is shown that the set of the constructed FHSs is optimalwith respect to the average Hamming correlation functions.

On the Hamming Auto- and Cross-correlation Functions of a Class of Frequency Hopping Sequences of Length $ p^{n} $