Orthogonal designs via computational algebra

Kotsireas, IS; Koukouvinos, C

dc.contributor.author	Kotsireas, IS	en
dc.contributor.author	Koukouvinos, C	en
dc.date.accessioned	2014-03-01T01:24:49Z
dc.date.available	2014-03-01T01:24:49Z
dc.date.issued	2006	en
dc.identifier.issn	1063-8539	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17454
dc.subject	Algorithms	en
dc.subject	Computational algebra	en
dc.subject	Gröbner bases	en
dc.subject	Hadamard matrices	en
dc.subject	Orthogonal designs	en
dc.subject	Supercomputing	en
dc.subject.classification	Mathematics	en
dc.subject.other	HADAMARD-MATRICES	en
dc.title	Orthogonal designs via computational algebra	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/jcd.20108	en
heal.identifier.secondary	http://dx.doi.org/10.1002/jcd.20108	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	We detail the Williamson array construction based on quaternions, following the description by Baumert and Hall. By analogy, we extend the construction to larger arrays using matrix representations of the algebras of octonions and sedenions. In the case of octonions, we obtain the full orthogonal design OD(8; 1, 1, 1, 1, 1, 1, 1, 1) or order 8 with 8 variables. In the case of sedenions we obtain the full orthogonal design OD(16; 1, 1, 7, 7) of order 16 with 4 variables and the full orthogonal design OD(16; 1, 1, 2, 2, 2, 2, 2, 2, 2) of order 16 with 9 variables. We use OD(16; 1, 1, 2, 2, 2, 2, 2, 2, 2) to search for inequivalent Hadamard matrices of orders 112, 144, 176 and we establish constructively three new lower bounds for the numbers of inequivalent Hadamard matrices of these three orders. (C) 2006 Wiley Periodicals, Inc.	en
heal.publisher	JOHN WILEY & SONS INC	en
heal.journalName	Journal of Combinatorial Designs	en
dc.identifier.doi	10.1002/jcd.20108	en
dc.identifier.isi	ISI:000239904100002	en
dc.identifier.volume	14	en
dc.identifier.issue	5	en
dc.identifier.spage	351	en
dc.identifier.epage	362	en