Rings and constructions of partial difference sets
type: Item
instance of: scholarly article
title: Rings and constructions of partial difference sets
zbMATH Open document ID: 1022.05010
DOI: 10.1016/S0012-365X(02)00832-4
author: Xiang-Dong Hou
published in: Discrete Mathematics
publication date: 2003-09-04T00:00:00Z
review text: The purpose of the paper is to construct (and better understand) PDSs on nonelementary abelian groups (and even with nonelementary Sylow subgroups). Let \(R\) be a finite Frobenius local ring with maximal ideal \(M\), and let \(I\) be a proper ideal of \(R\). Under suitable conditions a reversible PDS on (the additive group of) \(M/I\times M/I\) can be extended to a PDS on \(R/I\times R/I\). A second construction shows that in several cases a reversible PDS on \(M/r(M)\times R/r(M)\) (where \(r(M)\) is the right annihilator of \(M\) in \(R\)) can be extended to \(R\times R\). The third construction uses a chain ring, i.e. a ring \(R\) whose left ideals form a chain. Proofs are complex but very interesting and evocative; suggestions for natural questions and enlightening examples are given.
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 1974990
zbMATH Keywords: chain rings
zbMATH Keywords: finite Frobenius rings
zbMATH Keywords: local rings
zbMATH Keywords: Galois rings
zbMATH Keywords: generating characters
zbMATH Keywords: extensions of partial difference sets
zbMATH Keywords: Nakayama automorphisms
zbMATH Keywords: bent functions
zbMATH Keywords: reversible partial difference sets
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1974990