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How to generate all 8×8 cyclic matrix $A$ with the first row $(a_0, a_1, \ldots, a_7)$,

the matrix $A\in GL(8, 2)$ and the first row $a_0 + a_1 + \ldots + a_7 \neq 0$

How to generate all 8×8 cyclic matrix $A$ with the first row $(a_0, a_1, \ldots, a_7)$,

the matrix $A\in GL(8, 2)$ and the first row $a_0 + a_1 + \ldots + a_7 \neq 0$