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

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

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Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication horn 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 Drawing Tablet case, is minimized.Additionally, the new sets of FHSs achieve an optimal size in relation to a known theoretical bound.