Biangular vectors

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dc.contributor.authorBest, Darcy
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorKharaghani, Hadi
dc.date.accessioned2014-10-24T22:47:27Z
dc.date.available2014-10-24T22:47:27Z
dc.date.issued2013
dc.degree.levelMastersen_US
dc.degree.levelMasters
dc.descriptionviii, 133 leaves ; 29 cmen_US
dc.description.abstractThis thesis introduces unit weighing matrices, a generalization of Hadamard matrices. When dealing with unit weighing matrices, a lot of the structure that is held by Hadamard matrices is lost, but this loss of rigidity allows these matrices to be used in the construction of certain combinatorial objects. We are able to fully classify these matrices for many small values by defining equivalence classes analogous to those found with Hadamard matrices. We then proceed to introduce an extension to mutually unbiased bases, called mutually unbiased weighing matrices, by allowing for different subsets of vectors to be orthogonal. The bounds on the size of these sets of matrices, both lower and upper, are examined. In many situations, we are able to show that these bounds are sharp. Finally, we show how these sets of matrices can be used to generate combinatorial objects such as strongly regular graphs and association schemes.en_US
dc.identifier.urihttps://hdl.handle.net/10133/3560
dc.language.isoen_CAen_US
dc.proquestyesNoen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, 2013en_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.subjectUnit weighing matricesen_US
dc.subjectHadamard matricesen_US
dc.subjectUnbiaseden_US
dc.subjectVectorsen_US
dc.subjectDissertations, Academicen_US
dc.subjectMutually unbiased weighing matrices
dc.titleBiangular vectorsen_US
dc.typeThesisen_US
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