Geodesic
Permutations induced by digit-permutable transformations of a~module over a~Galois ring of characteristic~4
Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 9-19.

Voir la notice de l'article provenant de la source Math-Net.Ru

New classes of nonlinear permutations on a vector space that can be represented by linear transformations of a module over a Galois ring of characteristic 4 are constructed. The system of coordinate functions of such permutation is an orthogonal system of polynomials over the field. Orthogonal systems of two quadratic functions and diagonal quadratic functions are described.
Mots-clés : digit-permutable matrix, DP-matrix, permutation
Keywords: Galois ring. 
@article{PDM_2014_1_a1,
     author = {A. V. Abornev},
     title = {Permutations induced by digit-permutable transformations of a~module over {a~Galois} ring of characteristic~4},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {9--19},
     publisher = {mathdoc},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_1_a1/}
}
TY  - JOUR
AU  - A. V. Abornev
TI  - Permutations induced by digit-permutable transformations of a~module over a~Galois ring of characteristic~4
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 9
EP  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_1_a1/
LA  - ru
ID  - PDM_2014_1_a1
ER  - 
%0 Journal Article
%A A. V. Abornev
%T Permutations induced by digit-permutable transformations of a~module over a~Galois ring of characteristic~4
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 9-19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2014_1_a1/
%G ru
%F PDM_2014_1_a1
A. V. Abornev. Permutations induced by digit-permutable transformations of a~module over a~Galois ring of characteristic~4. Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 9-19. http://geodesic.mathdoc.fr/item/PDM_2014_1_a1/

[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

[2] Lidl R., Niderraiter G., Konechnye polya, v. 1, Mir, M., 1988 | Zbl

[3] Kuzmin A. S., Nechaev A. A., “Lineinye rekurrentnye posledovatelnosti nad koltsami Galua”, Algebra i Logika, 34:2 (1995), 169–189 | MR | Zbl

[4] Nikonov V. G., Sarantsev A. V., “O slozhnosti realizatsii v bazise DNF regulyarnykh sistem bulevykh funktsii”, Matematicheskie voprosy kriptografii, 1:3 (2010), 45–65

[5] Diedonné J. -A., La Géometrie des Groupes Classiques, Ergebnisse der Mathematik und ihrer Grenzgebiete, 5, Springer, 1971 | MR

[6] Kuzmin A. S., Nechaev A. A., “Trace-function on a Galois ring in coding theory”, LNCS, 1255, 1997, 277–290 | MR | Zbl