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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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Circulant matrix inverse in $GF(p)$
For a polynomial $C(x)=c_0+\dots+c_n x^n$, consider a circulant matrix $C$ such that
$$
C= \begin{pmatrix}
c_0 & c_{n-1} & \cdots & c_2 & c_1 \\
c_1 & c_0 & c_{n-1} & & …