New classes of residue supplementary difference systems
type: Item
instance of: scholarly article
title: New classes of residue supplementary difference systems
zbMATH Open document ID: 0884.05021
author: Anie Chaderjian
published in: Journal of Combinatorial Theory. Series A
publication date: 1998-04-01T00:00:00Z
review text: Difference sets have been studied extensively. The known examples fall into several families together with some sporadic exceptions. Supplementary difference systems are generalizations of difference sets. The author considers such generalizations of the residue difference sets. He establishes the existence of several new classes of supplementary difference systems which can be seen as corresponding to the family of difference sets. The major result is the existence of several new infinite families of supplementary difference systems which are unions of residue classes. More precisely, the multiplicative groups \(F^*_{q^2}\), where \(q= 4m+3\) is a prime power, are considered. Further it is proven that the union of certain cosets of the \((q+1)\)st powers in \(F^*_{q^2}\) form a supplementary difference system in the additive group of \(F_{q^2}\). Finally an application to both coding theory and Hadamard matrices is given.
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 1093097
zbMATH Keywords: difference sets
zbMATH Keywords: residue difference sets
zbMATH Keywords: supplementary difference systems
zbMATH Keywords: coding theory
zbMATH Keywords: Hadamard matrices
reviewed by: Ratnakaram Nava Mohan
MaRDI profile type: Publication
full work available at URL: jcta.1997.2803
OpenAlex ID: W1963680280
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DOI: 10.1006/JCTA.1997.2803
description: scientific article; zbMATH DE number 1093097