Properties of coordinate functions for a class of permutations on $\mathbb F_2^n$

In the class $\mathcal F_n$ of permutations on $\mathbb F_2^n$ with coordinate functions depending on all variables, we consider the subclass $\mathcal K_n$, where each permutation is obtained from the identity by $n$ independent transpositions. For permutations in $\mathcal K_n$, some cryptographic properties of coordinate functions $f_i$ are given, namely, $\operatorname{deg}f_i=n-1$, non-linearity $N_{f_i}=2$, correlation immunity order $\operatorname{cor}(f_i)=0$, algebraic immunity $\operatorname{AI}(f_i)=2$. The cardinalities $|\mathcal K_n|$ for $n=3,\dots,6$ has been presented.