Optimal One-Coincidence Sequence Sets with a Large Alphabet and Prime Length
Jin-Ho Chung, Duehee Lee, Dongsup Jin · Mathematics · 2026
The performance of a frequency-hopping spread-spectrum system is mainly dependent on the mathematical properties of its hopping sequences, which are designed to minimize interference between different users. The one-coincidence sequence frequency-hopping sequence (OC-FHS) set is one of the primary types, because it achieves the lowest possible values regarding Hamming auto- and cross-correlation. In this work, we propose an OC-FHS set of a prime length p and alphabet size pq for two primes p and q using a block structure modulo pq. In particular, when p=q, our construction provides a significantly larger set size compared with a previously known OC-FHS set with the same length and the same alphabet size. Moreover, the set size is optimal with respect to the bound established by Cao, Ge, and Miao. This extended set size can be applied to FHMA systems that need to accommodate a large number of users.