Amicable T-matrices and applications
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Date
2012
Authors
Gholamiangonabadi, Hamed
Journal Title
Journal ISSN
Volume Title
Publisher
Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2012
Abstract
Our main aim in this thesis is to produce new T-matrices from the set of existing
T-matrices. In Theorem 4.3 a multiplication method is introduced to generate new
T-matrices of order st, provided that there are some specially structured T-matrices
of orders s and t. A class of properly amicable and double disjoint T-matrices are
introduced. A number of properly amicable T-matrices are constructed which includes
2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 18, 22.
To keep the new matrices disjoint an extra condition is imposed on one set of
T-matrices and named double disjoint T-matrices. It is shown that there are some
T-matrices that are both double disjoint and properly amicable. Using these matrices
an infinite family of new T-matrices are constructed.
We then turn our attention to the application of T-matrices to construct orthogonal
designs and complex Hadamard matrices.
Using T-matrices some orthogonal designs constructed from 16 circulant matrices
are constructed. It is known that having T-matrices of order t and orthogonal designs
constructible from 16 circulant matrices lead to an infinite family of orthogonal designs.
Using amicable T-matrices some complex Hadamard matrices are shown to exist.
Description
iii, 49 leaves ; 29 cm
Keywords
T-matrix , Hadamard matrices , Matrices , Dissertations, Academic