Partial Difference Sets with Paley Parameters Ka

@inproceedings{Leung1995PartialDS,
  title={Partial Difference Sets with Paley Parameters Ka},
  author={H B Leung and SIU LUN},
  year={1995}
}
Partial difference sets with parameters (v,k,k,/x) = (v,(v— l)/2,(v — 5)/4,(v— l)/4) are called Paley partial difference sets. By using finite local rings, we construct a family of Paley PDSs for abelian/7-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 to Zpr x Zpr where p is an odd prime. 

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