Amicable matrices and orthogonal designs

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dc.contributor.authorChowdhury, S M Erfanul Kabir
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorKharaghani, Hadi
dc.date.accessioned2015-07-30T19:15:01Z
dc.date.available2015-07-30T19:15:01Z
dc.date.issued2015
dc.degree.levelMastersen_US
dc.description.abstractThis thesis is mainly concerned with the orthogonal designs of Baumert-Hall array type, OD(4n;n,n,n,n) where n=2k, k is odd integer. For every odd prime power p^r, we construct an infinite class of amicable T-matrices of order n=p^r+1 in association with negacirculant weighing matrices W(n,n-1). In particular, for p^r≡1 (mod 4) we construct amicable T-matrices of order n≡2 (mod 4) and application of these matrices allows us to generate infinite class of orthogonal designs of type OD(4n;n,n,n,n) and OD(4n;n,n,n-2,n-2) where n=2k; k is odd integer. For a special class of T-matrices of order n where each of T_i is a weighing matrix of weight w_i;1 ≤i≤4 and Williamson-type matrices of order m, we establish a theorem which produces four circulant matrices in terms of four variables. These matrices are additive and can be used to generate a new class of orthogonal design of type OD(4mn;w_1s,w_2s,w_3s,w_4s ); where s=4m. In addition to this, we present some methods to find amicable matrices of odd order in terms of variables which have an interesting application to generate some new orthogonal designs as well as generalized orthogonal designs.en_US
dc.description.sponsorshipUniversity of Lethbridge, NSERCen_US
dc.embargoNoen_US
dc.identifier.urihttps://hdl.handle.net/10133/3721
dc.language.isoen_CAen_US
dc.proquest.subject0405en_US
dc.proquestyesYesen_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.subjectHadamard matrixen_US
dc.subjectamicable t-matricesen_US
dc.subjectorthogonal designen_US
dc.subjectBaumert-Hall arrayen_US
dc.titleAmicable matrices and orthogonal designsen_US
dc.typeThesisen_US
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