Partial Difference Sets with Paley Parameters | Zendy

Leung Ka Hin | Zendy; Ma Siu Lun | Zendy

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Partial Difference Sets with Paley Parameters

Author(s) -

Leung Ka Hin,

Ma Siu Lun

Publication year - 1995

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/27.6.553

Subject(s) - mathematics , abelian group , prime (order theory) , rank (graph theory) , exponent , pure mathematics , combinatorics , group (periodic table) , chemistry , philosophy , linguistics , organic chemistry

Partial difference sets with parameters (ν, k ,λ,μ) = (ν,(ν − 1)/2, (ν − 5)/4,(ν − 1)/4) are called Paley partial difference sets. By using finite local rings, we construct a family of Paley PDSs for abelian p ‐groups with any given exponent. Furthermore, we prove some non‐existence results on Paley PDSs. Using these results, we prove that Paley PDSs exist in a rank 2 abelian group if and only if the group is isomorphic toℤ p r× ℤ p rwhere p is an odd prime.

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