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

In this paper, a new class of frequency hopping sequences (FHSs) of length p is constructed by using Ding-Helleseth generalized cyclotomic classes of order 2, of which the Hamming autoand crosscorrelation functions are investigated (for the Hamming cross-correlation, only the case p ≡ 3 (mod 4) is considered). It is shown that the set of the constructed FHSs is optimal with respect to the average Hamming correlation functions. key words: frequency hopping sequences, Hamming cross-correlation function, Ding-Helleseth generalized cyclotomic classes.