A construction of finite Frobenius rings and its application to partial difference sets

DOI10.1016/j.jalgebra.2006.07.034zbMath1113.05019OpenAlexW1978924472MaRDI QIDQ875072

Xiang-Dong Hou, Alexander A. Nechaev

Publication date: 11 April 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.07.034

zbMATH Keywords

partial difference setfinite Frobenius ringfinite local ring

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Related Items

Packings of partial difference sets ⋮ Euclidean self-dual codes over non-commutative Frobenius rings ⋮ A ring theoretic construction of Hadamard difference sets in \(\mathbb Z^n_8 \times \mathbb Z^n_2\) ⋮ Rings and constructions of partial difference sets ⋮ Non-existence of partial difference sets in abelian groups of order \(8p^3\) ⋮ Lattice of ideals of the polynomial ring over a commutative chain ring ⋮ Paley type group schemes and planar Dembowski-Ostrom polynomials ⋮ Finite Rings with Applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Translation nets and fixed-point-free group automorphisms
• Partial difference sets
• A survey of partial difference sets
• Rings and constructions of partial difference sets
• Bent functions, partial difference sets, and quasi-Frobenius local rings
• 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
• Duality for modules over finite rings and applications to coding theory
• New partial difference sets in p‐groups
• Partial Difference Sets with Paley Parameters
• New partial difference sets in \(\mathbb{Z}_{p^2}^t\) and a related problem about Galois rings
• Characterization of finite Frobenius rings