Difference sets in Abelian 2-groups

DOI10.1016/0097-3165(91)90050-QzbMath0746.05012OpenAlexW2049065660MaRDI QIDQ1175955

James A. Davis

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0097-3165(91)90050-q

zbMATH Keywords

Abelian difference setsAbelian 2-groups

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Finite nilpotent groups, (p)-groups (20D15)

Related Items (18)

Difference sets over the Galois ring \(\text{GR}(2^n,2)\) ⋮ The combinatorics of binary arrays ⋮ Hadamard difference sets in nonabelian 2-groups with high exponent ⋮ Constructions of difference sets in nonabelian 2-groups ⋮ Relative \((p^a, p^b, p^a, p^{a-b})\)-difference sets: A unified exponent bound and a local ring construction ⋮ Using rational idempotents to show Turyn's bound is sharp ⋮ A generalization of Kraemer's result on difference sets ⋮ Generalized perfect arrays and Menon difference sets ⋮ Proof of a conjecture on Hadamard 2-groups ⋮ Constructions of Butson Hadamard matrices invariant under abelian \(p\)-groups ⋮ On abelian \((2^{2m+1}(2^{m - 1}+1),2^{m}(2^{m}+1),2^{m})\)-difference sets ⋮ Generalized constructions of Menon-Hadamard difference sets ⋮ The structure of the abelian groups containing McFarland difference sets ⋮ Recent progress in algebraic design theory ⋮ New semiregular divisible difference sets ⋮ A construction of difference sets in high exponent 2-groups using representation theory ⋮ Nonexistence of certain perfect arrays ⋮ Perfect binary arrays and difference sets

Cites Work

• Variations on a scheme of McFarland for noncyclic difference sets
• A summary of noncylic difference sets, \(k<20\)
• Character sums and difference sets
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