New Families of Frequency-Hopping Sequences of Length mN Derived from the k-Fold Cyclotomy
Let N = p 1 ⋯ p k where p i , 1 ≤ i ≤ k, are odd primes such that p 1 < ⋯ < p k and p i = 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 m with 2 ≤ m ≤ M 1. The FHS sets constructed in this paper have new parameters not covered in the literature.
KeywordsCyclotomic numbers frequency-hopping sequences generalized cyclotomy Hamming correlation interleaved sequences
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