# MDS matrix

Let ${\displaystyle {\tilde {A}}=\left({\begin{array}{c}{\rm {Id}}_{n}\\\hline {\rm {A}}\end{array}}\right)}$ be the matrix obtained by joining the identity matrix Idn to A. Then a necessary and sufficient condition for a matrix A to be MDS is that every possible n×n submatrix obtained by removing m rows from ${\displaystyle {\tilde {A}}}$ is non-singular. This is also equivalent to the following: all the sub-determinants of the matrix A are non-null. Then a binary matrix A (namely over the field with two elements) is never MDS unless it has only one row or only one column with all components 1.