On the Hamming Auto- and Cross-correlation Functions of a Class of Frequency Hopping Sequences of Length $ p^{n} $
This work addresses the design of optimal frequency hopping sequences for communication systems, but it is incremental as it builds on existing cyclotomic methods.
The paper constructs a new class of frequency hopping sequences of length p^n using Ding-Helleseth generalized cyclotomic classes of order 2, and shows that the set is optimal with respect to average Hamming correlation functions, with analysis covering Hamming auto-correlation and cross-correlation for p ≡ 3 (mod 4).
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.