Bent functions, partial difference sets, and quasi-Frobenius local rings
type: Item
instance of: scholarly article
title: Bent functions, partial difference sets, and quasi-Frobenius local rings
zbMATH Open document ID: 0960.05028
DOI: 10.1023/A:1008322008395
author: Xiang-Dong Hou
published in: Designs, Codes and Cryptography
publication date: 2001-05-17T00:00:00Z
review text: Up to now, bent functions were studied only over elementary abelian groups. The author generalizes this concept to arbitrary finite abelian groups. He then gives a characterization of finite quasi-Frobenius local rings as those finite rings which have a unique minimal (non-zero) ideal. The main part of the paper uses a maximal ideal \(M\) of such a ring \(R\) to extend bent functions and certain partial difference sets defined on \(M\times M\) to corresponding objects on \(R\times R\); in particular, he provides an inductive extension procedure for such objects over finite chain rings.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 16L60
zbMATH DE Number: 1515342
zbMATH Keywords: bent functions
zbMATH Keywords: quasi-Frobenius local rings
zbMATH Keywords: partial difference sets
MaRDI profile type: Publication
full work available at URL: a:1008322008395
OpenAlex ID: W1565388220
description: scientific article; zbMATH DE number 1515342