Properties of substitutions generated by a class of filtering generators

We consider a class of substitutions on a set of binary strings of length $n$ whose coordinate functions are equivalent with respect to the transformation implemented by the affine shift register. We describe nonlinear Boolean functions $f$ depending significantly only on the first three variables and affine feedback functions $l$ of the shift register such that this shift register along with the filter function $f$ generates a system of coordinate functions of substitution. The degree of nonlinearity and the difference characteristic for substitutions from this class are calculated. By means of these substitutions a class of nonlinear shift registers of period $2^n-1$ is constructed.