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On good matrices, skew Hadamard matrices and optimal designs

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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


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