Properties of the output sequence of a simplest 2-linear shift register over $\mathbf Z_{2^n}$

The output sequence of a simplest self-controlled 2-linear shift register over the residue ring $R=\mathbf Z_{2^n}$ is considered. For a fixed output function we study the rank and the period of the output sequence. In some special cases frequency characteristics of cycles of the first coordinate sequence of the output sequence are considered. It is shown that the rank of the output sequence of the 2-dimensional shift register is much greater than the rank of the output sequence of a 1-dimensional register of the same length.