About the components of some classes of in-vertible vectorial boolean functions

In the class of invertible vectorial Boolean functions in n variables with coordinate functions depending on all variables, we consider the subclasses K_n and Kn, the functions in which are obtained using n independent transpositions, respectively, from the identity permutation and from the permutation, each coordinate function of which essentially depends on some one variable. It is shown that, for any F = (f₁... f_n) £ K_n U K'_n and i = 1,..., n, the coordinate function f_i has a single linear variable, the component function vF has no nonessential and linear variables for each vector v £ Fn weight of which is greater than 1, the nonlinearity, the degree, and the component algebraic immunity are 2, n - 1, and 2 respectively.

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