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A circulant matrix is a square matrix where each row has the same elements as the previous row, cyclically rotated right by one element. It is a specific kind of a square Toeplitz matrix.
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Are there infinite constructions for partial circulant Hadamard matrices?
I believe that the circulant Hadamard conjecture (that there are no circulant Hadamard matrices of size greater than $4\times4$) is still open.
I also know that examples of $(n/2) \times n$ matrices …