Correction to: On generalizations of differential uniform permutations over finite fields based on 2-to-1 mappings

o r g / 1 0 . 1 0 0 7 / s 0 0 2 0 0 -0 2 5 -0 0 6 9 1 -9A careful re-examination of the original work indicates that certain mathematical imprecisions influenced the accuracy of some results.The following corrections are given in detail, using the same notation as in the original paper [1].Theorem [Thoerem 3.1 [1]], demonstrates that t(x) does not possess the PcN property when g(x) is nonlinear.To address both linear and nonlinear aspects of g(x), it is necessary that t(x) is a permutation.By imposing this permutation condition on t(x), the following result is established as Theorem 1.