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dc.contributor.supervisor Kharaghani, Hadi
dc.contributor.author Chowdhury, S M Erfanul Kabir
dc.contributor.author University of Lethbridge. Faculty of Arts and Science
dc.date.accessioned 2015-07-30T19:15:01Z
dc.date.available 2015-07-30T19:15:01Z
dc.date.issued 2015
dc.identifier.uri https://hdl.handle.net/10133/3721
dc.description.abstract This 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.sponsorship University of Lethbridge, NSERC en_US
dc.language.iso en_CA en_US
dc.publisher Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science en_US
dc.relation.ispartofseries Thesis (University of Lethbridge. Faculty of Arts and Science) en_US
dc.subject Hadamard matrix en_US
dc.subject amicable t-matrices en_US
dc.subject orthogonal design en_US
dc.subject Baumert-Hall array en_US
dc.title Amicable matrices and orthogonal designs en_US
dc.type Thesis en_US
dc.publisher.faculty Arts and Science en_US
dc.publisher.department Department of Mathematics and Computer Science en_US
dc.degree.level Masters en_US
dc.proquest.subject 0405 en_US
dc.proquestyes Yes en_US
dc.embargo No en_US


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