On the invertibility of vector boolean functions

The class F _n, _m, _k of invertible vector Boolean functions F : Fn ^ Fm with coordinate functions depending on the given number k variables is considered. It is proved that 1) these functions do not exist for any n = m and k = 2; 2) the functions of the class Fn n n- ₁ can (can not) be built from affine coordinate functions for even (odd) n; 3) if n,m, k = 0 then Fn+i = 0.

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