Relative ( p a , p b , p a , p a − b -Difference Sets: A Unified Exponent Bound and a Local Ring Construction
Identifieur interne : 000522 ( Main/Exploration ); précédent : 000521; suivant : 000523Relative ( p a , p b , p a , p a − b -Difference Sets: A Unified Exponent Bound and a Local Ring Construction
Auteurs : Siu Lun Ma [Singapour] ; Bernhard SchmidtSource :
- Finite Fields and Their Applications [ 1071-5797 ] ; 2000.
Abstract
We show that for an odd prime p the exponent of an abelian group of order pa+b containing a relative (pa, pb, pa, pa−b)-difference set cannot exceed p⌊a/2⌋+1. Furthermore, we give a new local ring construction of relative (q2u, q, q2u, q2u−1)-difference sets for prime powers q. Finally, we discuss an important open case concerning the existence of abelian relative (pa, p, pa, pa−1)-difference sets.
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DOI: 10.1006/ffta.1999.0254
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