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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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The number of unitary circulant matrices over a finite field $\mathbb{F}_{q^2}$

Let $\tau$ denote the permutation matrix corresponding to $(1,2,\ldots,n)$. Consider it first as an element of $\mathrm{M}_n(q^2)$. This matrix has minimal polynomial equal to $X^n-1$, which is equa …
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