Cyclic abelian varieties over finite fields in ordinary isogeny classes

Given an abelian variety $A$ defined over a finite field $k$, we say that $A$ is "cyclic" if its group $A(k)$ of rational points is cyclic. In this paper we give a bijection between cyclic abelian varieties of an ordinary isogeny class $\mathcal{A}$ with Weil polynomial $f_{\mathcal{A}}$ and some classes of matrices with integer coefficients and having $f_{\mathcal{A}}$ as characteristic polynomial.