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 Shorts using generalized cyclotomy.Our results reveal that the constructed FHSs exhibit a one-coincidence property, meaning that the smallest correlation between different FHSs, Pie Dish aside from the trivial case, is minimized.
Additionally, the new sets of FHSs achieve an optimal size in relation to a known theoretical bound.