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Changing Field of MDS Matrix Multiplication

cn flag

Assume we have an $n \times n$ MDS matrix, whose entries are among $m \times m$ binary matrices. Can we see this matrix as a $n \times n$ matrix with entries from $GF(2^m)$? How can we replace this matrix with AES's MixColumn matrix? Also is it the other way around possible?

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ph flag
Please see the answer of [this post](https://crypto.stackexchange.com/questions/83997/how-to-check-that-an-km-times-km-block-binary-matrix-is-an-mds-matrix-in-k/84186#84186).
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