Paley partial difference sets in groups of order \(n^{4}\) and \(9n^{4}\) for any odd \(n>1\)

DOI10.1016/j.jcta.2010.02.008zbMath1231.05030OpenAlexW1525304426MaRDI QIDQ1957958

John B. Polhill

Publication date: 27 September 2010

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2010.02.008

zbMATH Keywords

strongly regular graphdifference setpartial difference setHadamard difference setPaley Hadamard difference setPaley partial difference set

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Other designs, configurations (05B30) Finite abelian groups (20K01) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Related Items (15)

Cyclotomic association schemes of broad classes and applications to the construction of combinatorial structures ⋮ Packings of partial difference sets ⋮ Near-complete external difference families ⋮ A new family of partial difference sets in 3-groups ⋮ Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions ⋮ Paley type partial difference sets in abelian groups ⋮ Abelian and non-abelian Paley type group schemes ⋮ Non-existence of partial difference sets in abelian groups of order \(8p^3\) ⋮ Cyclotomic construction of strong external difference families in finite fields ⋮ Constructions of almost difference sets from finite fields ⋮ Paley type sets from cyclotomic classes and Aarasu-Dillon-Player difference sets ⋮ Paley type group schemes and planar Dembowski-Ostrom polynomials ⋮ New constructions of Hadamard matrices ⋮ New necessary conditions on (negative) Latin square type partial difference sets in abelian groups ⋮ New constructions of strongly regular Cayley graphs on abelian non \(p\)-groups

Cites Work

• Unnamed Item
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• Paley type partial difference sets in non \(p\)-groups
• Some results on skew Hadamard difference sets
• A special class of Williamson matrices and difference sets
• Some infinite classes of special Williamson matrices and difference sets
• Generalized perfect arrays and Menon difference sets
• Proof of a conjecture on Hadamard 2-groups
• On the existence of abelian Hadamard difference sets and a new family of difference sets
• A survey of partial difference sets
• Partial difference sets in \(p\)-groups
• Nested Hadamard difference sets
• A unifying construction for difference sets
• On Xia's construction of Hadamard difference sets
• Character sums and difference sets
• Decomposition fields of difference sets
• A Family of Difference Sets
• On Orthogonal Matrices
• Constructions of Hadamard difference sets

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