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Can anyone explain what a branch number is and how to calculate it? I have checked several books on matrices but it seems uncommon. In particular, the matrix:

$$02\quad 03\quad 01\quad 01$$ $$01\quad 02\quad 03\quad 01$$ $$01\quad 01\quad 02\quad 03$$ $$03\quad 01\quad 01\quad 02$$

These entries are hexadecimals (or bytes), e.g. in bits ${02}$ is $00000010$, and comes from the Mix column layer in the $AES$ cipher (just in case that makes a difference).

I have read this matrix has the maximum branch number of $n+1 = 5$, but I do not understand where this came from or what it means.

I also read this is an $MDS$ matrix and I think branch numbers and $MDS$ matrices are linked somehow but, again, I don't know how. I have looked for video tutorials on $MDS$ matrices and branch numbers but there is nothing for beginners.

A couple of simple examples for branch numbers and/or $MDS$ matrices would be really helpful.