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Orderly generation of Butson Hadamard matrices. (English) Zbl 1423.05034

Authors’ abstract: “In this paper Butson-type complex Hadamard matrices \(BH(n, q)\) of order \(n\) over the complex \(q\)th roots of unity are classified for small parameters by computer-aided methods. The results include a classification of \(BH(21, 3), BH(16, 4)\), and \(BH(14, 6)\) matrices. There are exactly 72, 1786763, and 167776 such matrices, respectively, up to monomial equivalence. Additionally, an example of a \(BH(14, 10)\) matrix is shown for the first time, and the nonexistence of \(BH(8, 15), BH(11, q)\) for \( q \in \{10, 14, 15\}\), and \(BH(13, 15)\) matrices is proved”.
Seven open problems conclude the paper.

MSC:

05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)

Software:

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References:

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