# Check if a matrix over finite fields is superregular

Is there any practical, efficient algorithm to check if a matrix over $$\mathbf{F}_{p^n}$$ is superregular?

It need not be theoretically polynomial, just roughly be implementable for $$n=32$$ and for matrices of approximate size $$20 \times 100$$.

Definition: A matrix is superregular if all its minors are non-singular.

In particular, I'm looking for a construction of block circulant matrices that are superregular.