A Combinatorial Construction for Strictly Optimal Frequency-Hopping Sequences

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. Strictly optimal FHSs are those FHSs with optimal partial Hamming autocorrelation irrespective of the correlation window length. In this paper, strictly optimal FHSs are investigated from a combinatorial approach. A generic connection between strictly optimal FHSs and disjoint cyclic perfect Mendelsohn difference families is established. By virtue of this connection, new strictly optimal FHSs are generated from some disjoint CPMDFs. These strictly optimal FHSs have new parameters not covered in the literature.