A class of frequency-hopping sequences set with a multiple of prime number length

Frequency-hopping spread spectrum (FHSS) systems, with properties of anti-jamming, anti-intercept, code division multiple access (CDMA), channel sharing, etc, are usually applied in military radio communication, mobile communication, modern radar and sonar echolocation systems. Frequency-hopping sequences (FHS) is an integral part of FHSS systems. Based on the cyclotomy over the finite field and the Chinese remainder theorem, a class of FHSs set with a multiple of prime number length is constructed and the Hamming correlations of the new set are derived by some basic properties of the cyclotomic numbers. The results show that the proposed set is optimal with respect to the Peng-Fan bound and each FHS of the set is optimal or near optimal with respect to the Lempel-Greenberger bound. Furthermore, the previous constructions of optimal FHS sets based on cyclotomy are special cases of this paper. © 2015, Chinese Institute of Electronics. All right reserved.