A pair of differences (x,y)(x,y) is a \emph{related differential} for a linear layer MM if, for every coordinate at both the input and the output, at least one of the two values vanishes or the two values coincide. Related differentials underlie the zero-difference attack on AES of Bardeh and Rijmen, and the question of which maximum distance separable (MDS) matrices admit them was raised by Daemen and Rijmen, who showed that every 4×44\times4 circulant MDS matrix does while some Hadamard ones do n