Relative \((p^a, p^b, p^a, p^{a-b})\)-difference sets: A unified exponent bound and a local ring construction
type: Item
instance of: scholarly article
title: Relative \((p^a, p^b, p^a, p^{a-b})\)-difference sets: A unified exponent bound and a local ring construction
zbMATH Open document ID: 0947.05011
author: Bernhard Schmidt
author: Siu Lun Ma
published in: Finite Fields and their Applications
publication date: 2000-06-22T00:00:00Z
review text: After a short interesting historical updating the authors show that the exponent of an abelian group of order \(p^{2c+b}\) (\(p\) odd prime) containing a relative \((p^{2c},p^b,p^{2c},p^{2c-b})\)-difference set cannot exceed \(p^{c+1}\). Using local principal ideal rings (= chain rings) relative \((q^{2u},q,q^{2u},q^{2u-1})\)-difference sets (\(q\) a prime power) are construed. One of the difficult cases for the existence of \((p^a,p,p^a,p^{a-1})\)-difference sets is discussed in detail. As usual in this type of research, details are important and interesting but too complex to be quoted.
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 1421405
zbMATH Keywords: relative difference sets
zbMATH Keywords: local principal ideal rings
zbMATH Keywords: exponent
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
full work available at URL: ffta.1999.0254
OpenAlex ID: W2474927973
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DOI: 10.1006/FFTA.1999.0254
description: scientific article; zbMATH DE number 1421405