Bijective mappings generated by filtering generator | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 1(23).

The paper deals with the methods for constructing bijective mappings B/, _L whose coordinate functions are defined by a great length shift register with a feedback function L(x ₁, x ₂,..., x _n) and with an output (filtering) nonlinear function f (x ₁, x ₂,..., x _k) depending on a small number k of its arguments (k ^ n). It is known that the orthogonality of the coordinate functions is equivalent to the bijectiveness of the mapping B/, _L. A method developed in the paper reduces the problem of bijectiveness of B/, _L for any n to the case of bounded n < n ₀. The method allows to build new infinite classes of bijective mappings B/, _L for nonlinear functions f depending on four, five or six variables. Earlier, similar results were known for a function f depending on three arguments. The results can be useful for constructing and proving statistical properties of random sequences generated on the basis of filter generators.