A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy

Abstract

Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication systems. In this paper, we propose a novel construction of FHSs using generalized cyclotomy. Our results reveal that the constructed FHSs exhibit a one-coincidence property, meaning that the smallest correlation between different FHSs, aside from the trivial case, is minimized. Additionally, the new sets of FHSs achieve an optimal size in relation to a known theoretical bound.

Keywords

• frequency-hopping sequence
• Hamming correlation
• Peng–Fan bound
• generalized cyclotomy