Partial Difference Sets with Paley Parameters

DOI10.1112/blms/27.6.553zbMath0839.05019OpenAlexW2072807603MaRDI QIDQ4863837

Ka Hin Leung, Siu Lun Ma

Publication date: 5 June 1996

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/blms/27.6.553

zbMATH Keywords

partial difference setsabelian \(p\)-groupsfinite local ringsPaley parametersPaley PDSs

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Related Items (27)

A survey of partial difference sets ⋮ Packings of partial difference sets ⋮ Construction and nonexistence of strong external difference families ⋮ Negative Latin square type partial difference sets and amorphic association schemes with Galois rings ⋮ A construction of finite Frobenius rings and its application to partial difference sets ⋮ Near-complete external difference families ⋮ Existence and non-existence results for strong external difference families ⋮ Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions ⋮ Edge connectivity in difference graphs and some new constructions of partial sum families ⋮ Rings and constructions of partial difference sets ⋮ Paley type partial difference sets in abelian groups ⋮ Abelian and non-abelian Paley type group schemes ⋮ A new product construction for partial difference sets ⋮ Partial sum quadruples and bi-abelian digraphs ⋮ Enumeration of isomorphism classes of extensions of \(p\)-adic fields. ⋮ A construction of partial difference sets in \(\mathbb{Z}_{p^ 2}\times \mathbb{Z}_{p^ 2}\times\cdots\times \mathbb{Z}_{p^ 2}\) ⋮ New partial difference sets in \(\mathbb{Z}_{p^2}^t\) and a related problem about Galois rings ⋮ A nonexistence result on difference sets, partial difference sets and divisible difference sets ⋮ Finite commutative chain rings ⋮ Constructions of semi-regular relative difference sets ⋮ Paley type group schemes and planar Dembowski-Ostrom polynomials ⋮ Paley type partial difference sets in non \(p\)-groups ⋮ Some results on skew Hadamard difference sets ⋮ Strongly regular tri-Cayley graphs ⋮ A family of partial difference sets with Denniston parameters in nonelementary abelian 2-groups ⋮ Strongly regular Cayley graphs over the group \({\mathbb Z}_{p^n}\oplus {\mathbb Z}_{p^n}\) ⋮ On the groups of units of finite commutative chain rings.

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