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 VHS Rewinders 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 Humidity Cover 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.