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Given $M \in GL(n,F_2)$ which is known to have a $k^{th}$ root. How can I find a root algorithmically? Can I find all roots?

Other than being invertible and having a $k^{th}$ root I know nothing of M.

If I'm lucky and it happens that $gcd(k, |GL(n,F_2)|)=1$ then I can find the root by raising $M$ to the appropriate power. I'm interested in solving it for the more general case.

(also, is there any software library that can do it for me?)

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    I'd start trying with k=2, and work from there.2011-04-10

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