Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound

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...

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Bibliographic Details
Main Authors: Leung, Ka Hin, Schmidt, Bernhard, Zhang, Tao
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2024
Subjects:
Mathematical Sciences
Exponent bound
Direct product difference sets
Online Access:https://hdl.handle.net/10356/174655
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Institution: Nanyang Technological University
Language: English
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Summary: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.

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