Nonlinear permutations of a vector space recursively generated over a galois ring of characteristic 4 | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).

For any integers r ^ 1 and m ^ 3, some class of nonlinear permutation of a vector space (GF(2 )) is constructed. Every permutation in the class is defined as a composition of two operations: (1) a linear recurring transformation with a characteristic polynomial F(x) over a Galois ring R of cardinality 2 and characteristic 4; and (2) taking the first digit in an element of R represented by a pair of elements from GF(2 ). A necessary and sufficient condition is pointed for F(x) of a certain type in the composition to provide the bijectiveness property of the composition.