Dissertation in the field of Information theory, Pekka Lampio
The title of thesis is Classification of difference matrices and complex Hadamard matrices
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The concept of orthogonality is simple yet powerful and it plays an important role in many fields of mathematics, science and engineering. Depending on the field, orthogonality can be thought of describing a variety of mathematical relations, such as, objects being perpendicular, uncorrelated or independent. When the objects being orthogonal are the rows of a matrix, one arrives at the concept of an ortho-gonal matrix.
In this thesis we investigate orthogonal matrices where the elements are complex numbers (complex Hadamard matrices) or members of a finite field (difference matrices) . Using computational methods we determine the existence or non-existence of these matrices with the given parameters. We also count number of the matrices and present some of their most important properties. In addition to these classification results, we describe a general computational method for clas-sification of these matrices.
While the results obtained in this work can be regarded as basic research the studied matrices have many important applications in various fields of science and engineering. For example, orthogonal matrices can be used in the design of error-correcting codes in telecommunications, they can be used in the design of factorial experiments in statistics, and they play an important role in quantum physics.
Opponent: Professor Reinhard Laue, Universität Bayreuth, Germany
Supervisor: Professor Patric Östergård, Aalto University School of Electrical Engineering, Department of Communications and Networking
Dissertation website
Contact information:
Pekka Lampio
p. 050 354 1064
pekka.lampio@aalto.fi