A modified power spectral density test applied to weighing matrices with small weight

Kotsireas, IS; Koukouvinos, C; Pardalos, PM

dc.contributor.author	Kotsireas, IS	en
dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Pardalos, PM	en
dc.date.accessioned	2014-03-01T01:34:54Z
dc.date.available	2014-03-01T01:34:54Z
dc.date.issued	2011	en
dc.identifier.issn	1382-6905	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20929
dc.subject	Algorithm	en
dc.subject	Sparsity	en
dc.subject	Support	en
dc.subject	Weighing matrices	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Circulants	en
dc.subject.other	Sparsity	en
dc.subject.other	Weighing matrices	en
dc.subject.other	Algorithms	en
dc.subject.other	Combinatorial optimization	en
dc.subject.other	Discrete Fourier transforms	en
dc.subject.other	Power spectral density	en
dc.subject.other	Spectral density	en
dc.subject.other	Supports	en
dc.subject.other	Weighing	en
dc.title	A modified power spectral density test applied to weighing matrices with small weight	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10878-010-9335-5	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10878-010-9335-5	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	The power spectral density test has been used for at least a decade in the search for many kinds of combinatorial matrices, such as weighing matrices for instance. In this paper we establish a modified power spectral density test that we apply to the search for weighing matrices of small weights constructed from two circulants. The main novelty of our approach is to define the Discrete Fourier Transform on the support of the first rows of the two circulants, thus exploiting the inherent sparsity of the problem. This new formalism turns out to be very efficient for small weights 9,18,36 and we find 10 new weighing matrices W(2.p,18) for prime p {37,47,53,59,61,67,73,79,83,97}. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization. © 2010 Springer Science+Business Media, LLC.	en
heal.publisher	SPRINGER	en
heal.journalName	Journal of Combinatorial Optimization	en
dc.identifier.doi	10.1007/s10878-010-9335-5	en
dc.identifier.isi	ISI:000296520200026	en
dc.identifier.volume	22	en
dc.identifier.issue	4	en
dc.identifier.spage	873	en
dc.identifier.epage	881	en