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arXiv · 2312.07989

Constructing linked systems of relative difference sets via Schur rings

Mikhail Muzychuk·Grigory Ryabov
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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 $p^2$. All constructions of new RDSs and their linked systems are based essentially on a usage of cyclotomic Schur rings.

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Mikhail Muzychuk, Grigory Ryabov. 2023-12-13. Constructing linked systems of relative difference sets via Schur rings. https://arxiv.org/abs/2312.07989

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