Association schemes and mutually unbiased Hadamard matrices
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Date
2015
Authors
Sasani, Sara
University of Lethbridge. Faculty of Arts and Science
Journal Title
Journal ISSN
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Publisher
Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science
Abstract
This thesis is an examination of the theory of association schemes. A part of this thesis
focuses on the relation between association schemes and different combinatorial objects.
Special attention is paid to the notion of Bose-Mesner algebra of an association scheme,
which leads us to eigenmatrices, Krein matrices, and intersection matrices. It is shown that
if an association scheme is imprimitive, it can be used to generate a quotient association
scheme. Different constructions are used to generate association schemes. This thesis
explains how to generate a new class of association schemes from mutually unbiased Bushtype Hadamard matrices (abbreviated as MUBH). This class of association schemes leads to an upper bound on the number of mutually unbiased Bush-type Hadamard matrices. Lastly, the existence of this class of association schemes results in the existence of sets of MUBH.
Description
Keywords
association scheme , Bush-type Hadamard matrices , combinatorics