Geodesic
On the period length of vector sequences generated by polynomials modulo prime powers
Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 57-61
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We give an upper bound on the period length for vector sequences defined recursively by systems of multivariate polynomials with coefficients in the ring of integers modulo a prime power.
Keywords: recurrence sequences, vector sequences, period length, polynomial functions, finite rings.
Mots-clés : polynomial permutations 
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N. G. Parvatov. On the period length of vector sequences generated by polynomials modulo prime powers. Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 57-61. http://geodesic.mathdoc.fr/item/PDM_2016_1_a4/

[1] Anashin V. S., “Uniformly distributed sequences of $p$-adic integers”, Discrete Math. Appl., 12:6 (2002), 527–590 | MR | Zbl

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

[3] Ermilov D. M., Kozlitin O. A., “Cyclic structure of a polynomial generator over the Galois ring”, Mathematical Aspects of Cryptography, 4:1 (2013), 27–57 (in Russian)

[4] Eichenauer-Herrmann J., Grothe H., Lehn J., “On the period length of pseudo random vector sequences generated by matrix generators”, Matematics of Computation, 52:185 (1989), 145–148 | DOI | MR | Zbl

[5] Marshall I. B., “On the extension of Fermat's theorem to matrices of order $n$”, Proc. Edinburgh Math. Soc., 5 (1939–1941), 85–91 | DOI

[6] Niven I., “Fermat's theorem for matrices”, Duke Math. J., 15 (1948), 823–826 | DOI | MR | Zbl