On \((p^ a,p^ b,p^ a,p^{a-b})\)-relative difference sets

DOI10.1023/A:1008674331764zbMath0880.05021MaRDI QIDQ1361463

Bernhard Schmidt

Publication date: 19 January 1998

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

zbMATH Keywords

abelian relative difference setssplitting difference sets

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Subgroups of abelian groups (20K27)

Related Items (13)

Enhanced criteria on differential uniformity and nonlinearity of cryptographically significant functions ⋮ On \((mn,n,mn,m)\) relative difference sets with \(\operatorname{gcd}(m,n)=1\) ⋮ A unifying construction for difference sets ⋮ Generalized bent functions into \(\mathbb{Z}_{p^k}\) from the partial spread and the Maiorana-McFarland class ⋮ Multiple characters transforms and generalized Boolean functions ⋮ Nonlinear functions in abelian groups and relative difference sets. ⋮ Bent and \(\mathbb{Z}_{2^k}\)-bent functions from spread-like partitions ⋮ Relative \((p^a, p^b, p^a, p^{a-b})\)-difference sets: A unified exponent bound and a local ring construction ⋮ Relative \((p^a,p^b,p^a,p^{a - b})\)-difference sets in \(p\)-subgroups of \(\mathrm{SL}(n,K)\) ⋮ Semiregular relative difference sets in 2-groups containing a cyclic subgroup of index 2 ⋮ On differential uniformity and nonlinearity of functions ⋮ Relative \((pn,p,pn,n)\)-difference sets with \(GCD(p,n)=1\) ⋮ On the nonexistence of semi-regular relative difference sets

Cites Work

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• Polynomial addition sets and polynomial digraphs
• On a theorem of Ganley
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• A new construction of circulant \(GH(p^ 2; \mathbb{Z}_ p)\)
• On a paper of Dembrowski and Ostrom
• On the structure of Abelian groups admitting divisible difference sets
• The structure of the abelian groups containing McFarland difference sets
• Relative difference sets, planar functions, and generalized Hadamard matrices
• Character sums and difference sets
• Constructions of Partial Difference Sets and Relative Difference Sets on p -Groups
• Cyclic Affine Planes
• Relative difference sets

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