New families of frequency-hopping sequences of length mN derived from the k-fold cyclotomy

Abstract

Let N = p(1) ... p(k) where p(i), 1 <= i <= k, are odd primes such that p(i) < ... < p(k) and m = M(i)f + 1 for some positive integers M(i) and f. In this paper, we construct frequency-hopping sequence (FHS) sets by using the properties of the k-fold cycltomy. We give FHS sets with length 2N and frequency set size (N - 1)/f, which are optimal with respect to the Peng-Fan bound if k = 1, and near-optimal if k >= 2. We also present near-optimal FHS sets with length mN and frequency set size (N - 1)/f + 1 for any integer in with 2 <= m <= M(1). The FHS sets constructed in this paper have new parameters not covered in the literature.