Geodesic
Nonlinear permutations of a~vector space recursively generated over a~Galois ring of characteristic~4
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 40-41.

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For any integers $r\geq1$ and $m\geq3$, some class of nonlinear permutation of a vector space $(\operatorname{GF}(2^r))^m$ 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 $2^{2r}$ and characteristic 4; and (2) taking the first digit in an element of $R$ represented by a pair of elements from $\operatorname{GF}(2^r)$. 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.
Mots-clés : digit-permutable polynomial, DP-polynomial
Keywords: Galois ring. 
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     author = {A. V. Abornev},
     title = {Nonlinear permutations of a~vector space recursively generated over {a~Galois} ring of characteristic~4},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
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A. V. Abornev. Nonlinear permutations of a~vector space recursively generated over a~Galois ring of characteristic~4. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 40-41. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a16/

[1] Nechaev A. A., Abornev A. V., “Nonlinear permutations on a space over a finite field induced by linear transformations of a module over a Galois ring”, Matematicheskie voprosy kriptografii, 4:2 (2013), 81–100