Orderly Generation of Butson Hadamard Matrices

Pekka H. J. Lampio*, Patric R. J. Ostergard, Ferenc Szollosi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


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 is an element of {10, 14, 15}, and BH(13, 15) matrices is proved.

Original languageEnglish
Pages (from-to)313-331
Number of pages19
JournalMathematics of Computation
Issue number321
Publication statusPublished - Jan 2020
MoE publication typeA1 Journal article-refereed




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