Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound
Suppose a (λn,n,λn,λ) relative difference set exists in an abelian group G=S×H, where |S|=λ, |H|=n2, gcd(λ,n)=1, and λ is self-conjugate modulo λn. Then λ is a square, say λ=u2, and exp(S) divides u by Turyn’s exponent bound. We classify all such relative difference sets with exp(S)=u. We also show...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2024
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| Online Access: | https://hdl.handle.net/10356/174655 |
| _version_ | 1826128128773193728 |
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| author | Leung, Ka Hin Schmidt, Bernhard Zhang, Tao |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Leung, Ka Hin Schmidt, Bernhard Zhang, Tao |
| author_sort | Leung, Ka Hin |
| collection | NTU |
| description | Suppose a (λn,n,λn,λ) relative difference set exists in an abelian group G=S×H, where |S|=λ, |H|=n2, gcd(λ,n)=1, and λ is self-conjugate modulo λn. Then λ is a square, say λ=u2, and exp(S) divides u by Turyn’s exponent bound. We classify all such relative difference sets with exp(S)=u. We also show that n must be a prime power if an abelian (λn,n,λn,λ) RDS with gcd(λ,n)=1 exists and λ is self-conjugate modulo n. |
| first_indexed | 2024-10-01T07:19:53Z |
| format | Journal Article |
| id | ntu-10356/174655 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:19:53Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1746552024-04-08T15:35:20Z Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound Leung, Ka Hin Schmidt, Bernhard Zhang, Tao School of Physical and Mathematical Sciences Mathematical Sciences Exponent bound Direct product difference sets Suppose a (λn,n,λn,λ) relative difference set exists in an abelian group G=S×H, where |S|=λ, |H|=n2, gcd(λ,n)=1, and λ is self-conjugate modulo λn. Then λ is a square, say λ=u2, and exp(S) divides u by Turyn’s exponent bound. We classify all such relative difference sets with exp(S)=u. We also show that n must be a prime power if an abelian (λn,n,λn,λ) RDS with gcd(λ,n)=1 exists and λ is self-conjugate modulo n. Submitted/Accepted version 2024-04-07T02:44:02Z 2024-04-07T02:44:02Z 2024 Journal Article Leung, K. H., Schmidt, B. & Zhang, T. (2024). Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound. Designs, Codes, and Cryptography. https://dx.doi.org/10.1007/s10623-024-01384-z 0925-1022 https://hdl.handle.net/10356/174655 10.1007/s10623-024-01384-z 2-s2.0-85188703333 en Designs, Codes, and Cryptography © 2024 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1007/s10623-024-01384-z. application/pdf |
| spellingShingle | Mathematical Sciences Exponent bound Direct product difference sets Leung, Ka Hin Schmidt, Bernhard Zhang, Tao Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound |
| title | Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound |
| title_full | Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound |
| title_fullStr | Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound |
| title_full_unstemmed | Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound |
| title_short | Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound |
| title_sort | classification of semiregular relative difference sets with gcd λ n 1 attaining turyn s bound |
| topic | Mathematical Sciences Exponent bound Direct product difference sets |
| url | https://hdl.handle.net/10356/174655 |
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