New families of Strictly optimal Frequency hopping sequence sets

TL;DR

This paper introduces new methods for constructing frequency hopping sequence sets with optimal partial Hamming correlation, using combinatorial designs and recursive techniques, leading to infinitely many optimal solutions.

Contribution

It presents novel direct and recursive constructions of FHS sets with optimal partial Hamming correlation using trace functions, discrete logarithm, and difference packings.

Findings

Constructed several balanced nested cyclic difference packings and relative difference packings.

Developed three recursive methods for FHS set construction.

Produced infinitely many strictly optimal FHS sets meeting Peng-Fan bounds.

Abstract

Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHS sets with optimal partial Hamming correlation. We present several direct constructions for balanced nested cyclic difference packings (BNCDPs) and balanced nested cyclic relative difference packings (BNCRDPs) such that both of them have a special property by using trace functions and discrete logarithm. We also show three recursive constructions for FHS sets with partial Hamming correlation, which are based on cyclic difference matrices and discrete logarithm. Combing these BNCDPs, BNCRDPs and three recursive constructions, we obtain infinitely many new strictly optimal FHS sets with respect to the Peng-Fan bounds.