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A generalization of the method of C. Carlet for constructing differentially 4-uniform permutations of binary vector spaces in even dimension 2 k  is suggested. It consists in restricting APN-functions in 2 k +1 variables to a linear manifold of dimension 2 k . The general construction of the method is proposed and a criterion for its applicability is established. Power permutations to which this construction is applicable are completely described and a class of suitable not one-to-one functions is presented.

A method of construction of differentially 4-uniform permutations over V m for even m