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 systems.In this paper, we propose a novel construction of FHSs using generalized cyclotomy.Our results Volumizer 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 SHEA NUT OIL FHSs achieve an optimal size in relation to a known theoretical bound.