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arXiv · 2110.12206

Some special complex Hadamard matrices of order six

Mengfan Liang·Lin Chen·Fengyue Long·Xinyu Qiu
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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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Mengfan Liang, Lin Chen, Fengyue Long, Xinyu Qiu. 2021-10-23. Some special complex Hadamard matrices of order six. https://arxiv.org/abs/2110.12206

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