Nonlinear permutations recursively generated over the Galois ring of characteristic 4

The class of nonlinear permutations $\pi_F$ of a space $\mathrm{GF}(2^r)^m$ of any dimension $m\ge3$ is constructed. Each permutation $\pi_F$ is recursively generated by the characteristic polynomial $F(x)$ over the Galois ring $\mathrm{GR}(2^{2r},4)$. Results of the paper by A. A. Nechaev and the author are generalized to an arbitrary Galois ring of characteristic 4.