Constructing linked systems of relative difference sets via Schur rings

2023/12/13 by Mikhail Muzychuk, Muzychuk, Mikhail, Grigory Ryabov +1
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Finite Group Theory Research #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2312.07989

Abstract

In the present paper, we study relative difference sets (RDSs) and linked systems of them. It is shown that a closed linked system of RDSs is always graded by a group. Based on this result, we also define a product of RDS linked systems sharing the same grading group. Further, we generalize the Davis-Polhill-Smith construction of a linked system of RDSs. Finally, we construct new linked system of RDSs in a Heisenberg group over a finite field and family of RDSs in an extraspecial p-group of exponent p². All constructions of new RDSs and their linked systems are based essentially on a usage of cyclotomic Schur rings.

Related

• Linking systems of difference sets
• New constructions for disjoint partial difference families and external partial difference families
• Linked systems of symmetric group divisible designs
• RGD-systems over \mathbbF₂
• Linked systems of symmetric group divisible designs of type II