Hadamard ideals and Hadamard matrices from two circulant submatrices

Kotsireas, IS; Koukouvinos, C

dc.contributor.author	Kotsireas, IS	en
dc.contributor.author	Koukouvinos, C	en
dc.date.accessioned	2014-03-01T01:56:19Z
dc.date.available	2014-03-01T01:56:19Z
dc.date.issued	2007	en
dc.identifier.issn	08353026	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/28052
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-77955052806&partnerID=40&md5=3ecee161b412179f16d901c64ec9e618	en
dc.subject	Algorithm	en
dc.subject	Computational algebra	en
dc.subject	Hadamard equivalence	en
dc.subject	Hadamard ideal	en
dc.subject	Hadamard matrices	en
dc.subject.other	Circulant submatrices	en
dc.subject.other	Computational algebra	en
dc.subject.other	Hadamard equivalence	en
dc.subject.other	Hadamard ideal	en
dc.subject.other	Hadamard matrices	en
dc.subject.other	Algorithms	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Computational methods	en
dc.subject.other	Heuristic methods	en
dc.subject.other	Matrix algebra	en
dc.title	Hadamard ideals and Hadamard matrices from two circulant submatrices	en
heal.type	journalArticle	en
heal.publicationDate	2007	en
heal.abstract	We apply Computational Algebra methods to the construction of Hadamard matrices from two circulant submatrices, given by C. H. Yang. We associate Hadamard ideals to this construction, to systematize the application of Computational Algebra methods. Our approach yields an exhaustive search for Hadamard matrices from two circulant submatrices for this construction, for the first eight admissible values 2, 4, 8, 10, 16, 18, 20, 26 and partial searches for the next three admissible values 32, 34 and 40. From the solutions we found, for the admissible values 26 and 34, we located new inequivalent Hadamard matrices of orders 52 and 68 with two circulant submatrices, thus improving the lower bounds for the numbers of inequivalent Hadamard matrices of orders 52 and 68. We also propose a heuristic decoupling of one of the equations arising from this construction, which can be used together with the PSD test to search for solutions more efficiently.	en
heal.journalName	Journal of Combinatorial Mathematics and Combinatorial Computing	en
dc.identifier.volume	61	en
dc.identifier.spage	97	en
dc.identifier.epage	110	en