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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.

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