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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.