Constructing linked systems of relative difference sets via Schur rings Full article
| Journal |
Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586 |
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| Output data | Year: 2024, Volume: 92, Pages: 2615–2637 Pages count : 23 DOI: 10.1007/s10623-024-01406-w | ||
| Tags | Relative difference sets · Linked systems · Schur rings | ||
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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 p2. All constructions of new RDSs and their linked systems make usage of cyclotomic Schur rings.
Cite:
Muzychuk M.
, Ryabov G.
Constructing linked systems of relative difference sets via Schur rings
Designs, Codes and Cryptography. 2024. V.92. P.2615–2637. DOI: 10.1007/s10623-024-01406-w WOS Scopus OpenAlex
Constructing linked systems of relative difference sets via Schur rings
Designs, Codes and Cryptography. 2024. V.92. P.2615–2637. DOI: 10.1007/s10623-024-01406-w WOS Scopus OpenAlex
Dates:
| Submitted: | Dec 18, 2023 |
| Accepted: | Mar 18, 2024 |
| Published online: | Apr 16, 2024 |
Identifiers:
| Web of science: | WOS:001287696700013 |
| Scopus: | 2-s2.0-85190516537 |
| OpenAlex: | W4394854257 |