Orderly generation of Butson Hadamard matrices

Lampio, Pekka H.J. and Östergård, Patric R.J. and Szőllősi, Ferenc (2019) Orderly generation of Butson Hadamard matrices. MATHEMATICS OF COMPUTATION. ISSN 0025-5718

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Abstract

In this paper Butson-type complex Hadamard matrices BH(n, q) of order n over the complex qth 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 E {10, 14, 15}, and BH(13, 15) matrices is proved.

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