On good matrices, skew Hadamard matrices and optimal designs

Georgiou, S; Koukouvinos, C; Stylianou, S

dc.contributor.author	Georgiou, S	en
dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Stylianou, S	en
dc.date.accessioned	2014-03-01T01:18:09Z
dc.date.available	2014-03-01T01:18:09Z
dc.date.issued	2002	en
dc.identifier.issn	0167-9473	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14819
dc.subject	Good matrices	en
dc.subject	Linear models	en
dc.subject	Optimal designs	en
dc.subject	Orthogonal designs	en
dc.subject	Skew Hadamard matrices	en
dc.subject	Supplementary difference sets	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Statistics & Probability	en
dc.subject.other	Algorithms	en
dc.subject.other	Fourier transforms	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Optimal designs	en
dc.subject.other	Data reduction	en
dc.subject.other	numerical model	en
dc.title	On good matrices, skew Hadamard matrices and optimal designs	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0167-9473(02)00067-1	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0167-9473(02)00067-1	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	In two-level factorial experiments and in other linear models the coefficients of the unknown parameters can take one out of two values. When the number of observations is a multiple of four, the D-optimal design is a Hadamard matrix. Skew Hadamard matrices are of special interest due to their use, among others, in constructing D-optimal weighing designs for n equivalent to 3(mod4). A method is given for constructing skew Hadamard matrices which is based on the construction of good matrices. The construction is achieved through an algorithm which is also presented and relies on the discrete Fourier transform. It is known that good matrices of order n, exist for all odd n less than or equal to 35 and n = 127. In this paper, we give for the first time all non-equivalent circulant good matrices of odd order 33 less than or equal to n less than or equal to 39. We note that no good matrices were previously known for orders 37 and 39. These are presented in a table in the form of the corresponding non-equivalent supplementary difference sets. In the sequel we use good matrices to construct some skew Hadamard matrices and orthogonal designs. (C) 2002 Elsevier Science B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Computational Statistics and Data Analysis	en
dc.identifier.doi	10.1016/S0167-9473(02)00067-1	en
dc.identifier.isi	ISI:000179253400010	en
dc.identifier.volume	41	en
dc.identifier.issue	1	en
dc.identifier.spage	171	en
dc.identifier.epage	184	en