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Construction, classification and parametrization of complex Hadamard matrices
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The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three chapters, each describing one of three distinct faces of this field whose treatment require various mathematical tools ranging from combinatorics, functional analysis to symbolic computation. Although we firmly believe that these beautiful objects are interesting on their own and worth investigating from a purely mathematical perspective we make considerable efforts to highlight some of their applications we aware of.
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Complex generalised weighing matrices in centraliser algebras of monomial representations
A computer census classifies complex generalised weighing matrices with primitive monomial symmetry of rank at most 5 and degree up to 80, producing new matrices, Hamming-scheme families, and quantum stabiliser codes.
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