Constructing linked systems of relative difference sets via Schur rings

Mikhail Muzychuk, Grigory Ryabov

Research output: Contribution to journalArticlepeer-review


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 make usage of cyclotomic Schur rings.

Original languageAmerican English
JournalDesigns, Codes, and Cryptography
StateAccepted/In press - 1 Jan 2024


  • 05B10
  • 05E30
  • 20C05
  • Linked systems
  • Relative difference sets
  • Schur rings

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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