Some special complex Hadamard matrices of order six
Mengfan Liang, Lin Chen, Fengyue Long, Xinyu Qiu

TL;DR
This paper advances the classification of 6x6 complex Hadamard matrices by characterizing specific subclasses with unique structural properties, contributing to the longstanding open problem in matrix theory.
Contribution
It provides a detailed characterization of several special classes of 6x6 complex Hadamard matrices, marking progress toward their complete classification.
Findings
Characterized CHMs with a 2x3 rank-one submatrix
Identified CHMs with three distinct elements and first row all ones
Analyzed H2-reducible CHMs with three distinct elements
Abstract
The complete classification of 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 submatrix with rank one, the CHMs containing exactly three distinct elements and all elements of the first row being one, the -reducible matrices containing exactly three distinct matrix elements, and the CHMs containing a 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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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Topics in Algebra · Mathematics and Applications
