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

##### Minglong Qi, Shenwu Xiong, Jingling Yuan

In this paper, a new class of frequency hopping sequences (FHSs) of length $p^{n}$ is constructed by using Ding-Helleseth generalized cyclotomic classes of order 2, of which the Hamming auto- and cross-correlation functions are investigated (for the Hamming cross-correlation, only the case $p\equiv 3\pmod 4$ is considered). It is shown that the set of the constructed FHSs is optimal with respect to the average Hamming correlation functions.

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