Hadamard ideals and Hadamard matrices with two circulant cores

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	2014-03-01T01:24:29Z
dc.date.available	2014-03-01T01:24:29Z
dc.date.issued	2006	en
dc.identifier.issn	0195-6698	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17278
dc.subject	Computer Algebra	en
dc.subject	Exhaustive Search	en
dc.subject	hadamard matrices	en
dc.subject.classification	Mathematics	en
dc.title	Hadamard ideals and Hadamard matrices with two circulant cores	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ejc.2005.03.004	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ejc.2005.03.004	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	We apply computational algebra methods to the construction of Hadamard matrices with two circulant cores, given by Fletcher, Gysin and Seberry. We introduce the concept of Hadamard ideal, to systematize the application of computational algebra methods for this construction. We use the Hadamard ideal formalism to perform exhaustive search constructions of Hadamard matt-ices with two circulant cores for the twelve orders 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52. The total number of such Hadamard matrices is proportional to the square of the parameter. We use the Hadamard ideal formalism to compute the proportionality constants for the twelve orders listed above. Finally, we use the Hadamard ideal formalism to improve the lower bounds for the number of inequivalent Hadamard matrices for the seven orders 44, 48, 52, 56, 60, 64, 68. (C) 2005 Elsevier Ltd. All rights reserved.	en
heal.publisher	ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD	en
heal.journalName	European Journal of Combinatorics	en
dc.identifier.doi	10.1016/j.ejc.2005.03.004	en
dc.identifier.isi	ISI:000236988800004	en
dc.identifier.volume	27	en
dc.identifier.issue	5	en
dc.identifier.spage	658	en
dc.identifier.epage	668	en