New Families of Frequency-Hopping Sequence Sets with Optimal Hamming Correlation

With the advantage of transmitting messages efficiently along with switching frequencies at set intervals by each user, frequency-hopping sequence (FHS) has been widely applied in the frequency-hopping multiple access spread spectrum systems. In such systems, the Hamming correlation property of FHS is an important standard to measure the system performance. In this paper, a combinatorial description of difference-balanced function from F-q(n)* onto F-q(m) is given, and the sizes of its preimage sets are determined without resorting to d-homogeneous property, where m and n are two positive integers with m|n. Afterwards, we construct new near-optimal FHSs and optimal FHS sets by virtue of the Chinese Remainder Theorem and d-homogeneous functions with difference-balanced property, which generalize some earlier constructions of optimal FHS sets and produce optimal FHS sets which are not covered in the foregoing literature.