An MDS matrix (maximum distance separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography. Technically, an m × n {\displaystyle m\times n} matrix A {\displaystyle A} over a finite field K {\displaystyle K} is an MDS matrix if it is the transformation matrix of a linear transformation f ( x ) = A x {\displaystyle f(x)=Ax} from K n {\displaystyle K^{n}} to K m {\displaystyle K^{m}} such that no two different ( m + n ) {\displaystyle (m+n)} -tuples of the form ( x , f ( x ) ) {\displaystyle (x,f(x))} coincide in n {\displaystyle n} or more components.Equivalently, the set of all ( m + n ) {\displaystyle (m+n)} -tuples reference
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