Geodesic
Estimate of the maximal cycle length in the graph of polynomial transformation of Galois--Eisenstein ring
Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 41-58.

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The paper is concerned with polynomial transformations of a finite commutative local principal ideal of a ring (a finite commutative uniserial ring, a Galois–Eisenstein ring). It is shown that in the class of Galois–Eisenstein rings with equal cardinalities and nilpotency indexes over Galois rings there exist polynomial generators for which the period of the output sequence exceeds those of the output sequences of polynomial generators over other rings.
Keywords: polynomial transformation, period, finite commutative uniserial ring. 
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O. A. Kozlitin. Estimate of the maximal cycle length in the graph of polynomial transformation of Galois--Eisenstein ring. Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 41-58. http://geodesic.mathdoc.fr/item/DM_2017_29_4_a2/

[1] Viktorenkov V.E., “O stroenii orgrafov polinomialnykh preobrazovanii nad konechnymi kommutativnymi koltsami s edinitsei”, Diskretnaya matematika, 29:3 (2017), 3–23 | DOI

[2] Glukhov M.M., Elizarov V.P., Nechaev A.A., Algebra, Uchebnik, 2-e izd., ispr. i dop., Lan, SPb., 2015, 608 pp.

[3] Elizarov V.P., Konechnye koltsa, Gelios – ARV, M., 2006, 304 pp.

[4] Ermilov D.M., Kozlitin O.A., “Tsiklovaya struktura polinomialnogo generatora nad koltsom Galua”, Matematicheskie voprosy kriptografii, 4:1 (2013), 27–57

[5] Ermilov D.M., Kozlitin O.A., “O stroenii grafa polinomialnogo preobrazovaniya koltsa Galua”, Matematicheskie voprosy kriptografii, 6:3 (2015), 47–73 | MR

[6] Larin M. V., “Transitive polynomial transformations of residue class rings”, Discrete Math. Appl., 12:2 (2002), 127–140 | DOI | DOI | MR | Zbl

[7] Nechaev A. A., “On the structure of finite commutative rings with an identity”, Math. Notes, 10:6 (1971), 840–845 | DOI | MR | Zbl

[8] Nechaev A. A., “Finite principal ideal rings”, Math. USSR-Sb., 20:3 (1973), 364–382 | DOI | MR | Zbl

[9] Slovar kriptograficheskikh terminov, eds. Pod red. B.A. Pogorelova i V.N. Sachkova, MTsNMO, M., 2006, 92 pp.

[10] Anashin V.S., “Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers”, J. Math. Sciences, 89:4 (1998), 1355–1390 | DOI | MR | Zbl