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Some special complex Hadamard matrices of order six

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arxiv 2110.12206 v1 pith:MZW7C3FF submitted 2021-10-23 math-ph math.MP

Mengfan Liang , Lin Chen , Fengyue Long , Xinyu Qiu This is my paper · ORCID
classification math-phmath.MP
keywords chmscontainingelementshadamardmatricestimesclassificationcomplete
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abstract

The complete classification of $6\times 6$ complex Hadamard matrices (CHMs) is a long-standing open problem. In this paper we investigate a series of CHMs, such as the CHMs containing a $2\times 3$ submatrix with rank one, the CHMs containing exactly three distinct elements and all elements of the first row being one, the $H_2$-reducible matrices containing exactly three distinct matrix elements, and the CHMs containing a $3\times 3$ Hadamard submatrix. We characterize all forms of these CHMs. Our results are the latest progress on the complete classification of CHMs.

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