New Classes of Optimal Frequency-Hopping Sequences by Interleaving Techniques

摘要

In this paper we construct new classes of optimal frequency-hopping sequences (FHSs) with respect to the Lempel–Greenberger bound and the Peng–Fan bound by interleaving techniques which are used to construct a sequence of length $kN$ from $k$ sequences of length $N$. We first give two generic constructions for optimal FHS sets from some known optimal FHS sets by interleaving techniques and present some examples of new optimal FHS sets. We then design new optimal FHSs whose parameters include those of the known optimal constructions with length $kN$ and frequency set size $N$ for some positive integers $k$ and $N$ . We also construct optimal FHS sets of length $kp$ from power-residue sequences for any odd prime $p$ and $2le k≪p$. In particular, our constructions give several new parameters not covered in the literature, which are summarized in Tables I and II .