Weighing matrices and string sorting

Kotsireas, IS; Koukouvinos, C; Seberry, J

dc.contributor.author	Kotsireas, IS	en
dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Seberry, J	en
dc.date.accessioned	2014-03-01T01:32:24Z
dc.date.available	2014-03-01T01:32:24Z
dc.date.issued	2009	en
dc.identifier.issn	0218-0006	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20114
dc.subject	Algorithm	en
dc.subject	Locations of zeros	en
dc.subject	Pattern	en
dc.subject	Power spectral density	en
dc.subject	Rounding error	en
dc.subject	Weighing matrices	en
dc.subject.classification	Mathematics, Applied	en
dc.title	Weighing matrices and string sorting	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00026-009-0027-8	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00026-009-0027-8	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	In this paper we establish a fundamental link between the search for weighing matrices constructed from two circulants and the operation of sorting strings, an operation that has been studied extensively in computer science. In particular, we demonstrate that the search for weighing matrices constructed from two circulants using the power spectral density criterion and exploiting structural patterns for the locations of the zeros in candidate solutions, can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. This allows us to bring into bear efficient algorithms from the string sorting literature. We also state and prove some new enhancements to the power spectral density criterion, that allow us to treat successfully the rounding error effect and speed up the algorithm. Finally, we use these ideas to find new weighing matrices of order 2n and weights 2n - 13, 2n - 17 constructed from two circulants. © Birkhäuser Verlag Basel/Switzerland 2009.	en
heal.publisher	BIRKHAUSER VERLAG AG	en
heal.journalName	Annals of Combinatorics	en
dc.identifier.doi	10.1007/s00026-009-0027-8	en
dc.identifier.isi	ISI:000271395800004	en
dc.identifier.volume	13	en
dc.identifier.issue	3	en
dc.identifier.spage	305	en
dc.identifier.epage	313	en