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

Abstract

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 $p\equiv 3(\mathrm{mod}4)$ is considered). It is shown that the set of the constructed FHSs is optimal with respect to the average Hamming correlation functions.