New negative Latin square type partial difference sets in nonelementary Abelian 2-groups and 3-groups

DOI10.1007/S10623-007-9165-3zbMath1185.05026OpenAlexW2082530386MaRDI QIDQ1008991

John B. Polhill

Publication date: 31 March 2009

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-007-9165-3

zbMATH Keywords

association schemespartial difference setLatin square type partial difference setnegative Latin square partial difference set

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Orthogonal arrays, Latin squares, Room squares (05B15) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Related Items (12)

Cyclotomic association schemes of broad classes and applications to the construction of combinatorial structures ⋮ Packings of partial difference sets ⋮ Negative Latin square type partial difference sets and amorphic association schemes with Galois rings ⋮ A new family of partial difference sets in 3-groups ⋮ Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions ⋮ A new product construction for partial difference sets ⋮ Some implications on amorphic association schemes ⋮ Strongly regular graphs associated with ternary bent functions ⋮ Paley type group schemes and planar Dembowski-Ostrom polynomials ⋮ Paley type partial difference sets in non \(p\)-groups ⋮ Strong difference families, difference covers, and their applications for relative difference families ⋮ New necessary conditions on (negative) Latin square type partial difference sets in abelian groups

Cites Work

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• Amorphic association schemes with negative Latin square-type graphs
• A survey of partial difference sets
• Constructions of nested partial difference sets with Galois rings
• Strongly regular decompositions of the complete graph
• Character sums and difference sets
• Constructions of partial difference sets and relative difference sets using Galois rings. II
• Constructions of Partial Difference Sets and Relative Difference Sets on p -Groups
• A computer application to finite p-groups
• NEGATIVE LATIN SQUARE TYPE PARTIAL DIFFERENCE SETS IN NONELEMENTARY ABELIAN 2-GROUPS

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