New Constructions of One-Coincidence Sequence Sets over Integer Rings

Abstract

In this paper, we introduce new constructions of one-coincidence frequency-hopping sequence (OC-FHS) sets over integer rings. These OC-FHSs are designed to minimize interference in frequency-hopping multiple access (FHMA) systems, which are widely used in various communication applications. By leveraging the properties of primitive elements in integer ring Zpn, we develop OC-FHS sets with lengths mpn−1 for m dividing (p−1), along with constructions with composite lengths based on linear functions. The proposed OC-FHS sets include parameters not previously addressed in the literature and encompass some known cases as special cases.

Keywords

• frequency-hopping
• hamming correlation
• primitive root
• pseudorandom sequence