Asymptotic existence of orthogonal designs

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dc.contributor.authorGhaderpour, Ebrahim
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorKharaghani, Hadi
dc.date.accessioned2014-10-30T20:21:34Z
dc.date.available2014-10-30T20:21:34Z
dc.date.issued2013
dc.degree.levelPh.Den_US
dc.degree.levelPhD
dc.descriptionv, 115 leaves ; 29 cm
dc.description.abstractAn orthogonal design of order n and type (si,..., se), denoted OD(n; si,..., se), is a square matrix X of order n with entries from {0, ±x1,..., ±xe}, where the Xj’s are commuting variables, that satisfies XX* = ^ ^g=1 sjx^j In, where X* denotes the transpose of X, and In is the identity matrix of order n. An asymptotic existence of orthogonal designs is shown. More precisely, for any Atuple (s1,..., se) of positive integers, there exists an integer N = N(s1,..., se) such that for each n > N, there is an OD(2n(s1 + ... + se); 2ns1,..., 2nse). This result of Chapter 5 complements a result of Peter Eades et al. which in turn implies that if the positive integers s1, s2,..., se are all highly divisible by 2, then there is a full orthogonal design of type (s1, s2,..., se). Some new classes of orthogonal designs related to weighing matrices are obtained in Chapter 3. In Chapter 4, we deal with product designs and amicable orthogonal designs, and a construction method is presented. Signed group orthogonal designs, a natural extension of orthogonal designs, are introduced in Chapter 6. Furthermore, an asymptotic existence of signed group orthogonal designs is obtained and applied to show the asymptotic existence of orthogonal designs.en_US
dc.identifier.urihttps://hdl.handle.net/10133/3595
dc.language.isoen_CAen_US
dc.proquestyesNoen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectorthogonal designen_US
dc.subjectasymptotic existenceen_US
dc.subjectweighing matricesen_US
dc.subjectAlgebras, Linear
dc.subjectMathematical analysis
dc.subjectAsymptotic expansions
dc.subjectMatrices
dc.subjectHadamard matrices
dc.subjectDissertations, Academic
dc.titleAsymptotic existence of orthogonal designsen_US
dc.typeThesisen_US
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