Optimal Frequency-Hopping Sequence Sets Based on Cyclotomy

In this paper, a kind of generalized cyclotomy with respect to the square of a prime is presented and the properties of the corresponding generalized cyclotomic numbers are investigated. Based on the generalized cyclotomy, a class of frequency-hopping sequence (FHS) set is constructed. By means of some basic properties of the generalized cyclotomy, we derive the Hamming correlation distribution of the new set. The results show that the proposed FHS set is optimal with regard to the average Hamming correlation (AHC) bound. By choosing suitable parameters, the construction also leads to the optimal FHS set and the optimal FHSs with regard to the maximum Hamming correlation (MHC) bound and Lempel-Greenberger bound, respectively.