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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?

Let $r\mbox{-}H(k\times n)$ denote a $k\times n$ partial circulant Hadmard matrix in which a row (and hence all) sums to $r$. It's a known result, see Theroem 9 in [1], that $2\mbox{-}H((p+1)\times 2( …
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