On the structure of digraphs of polynomial transformations over finite commutative rings with unity

References

[1] Anashin V. S., “Uniformly distributed sequences of p-adic integers”, Math. Notes, 55:2 (1994), 109–133.10.1007/BF02113290Suche in Google Scholar

[2] Knuth D., The Art of Computer Programming, Addison Wesley, 1969, 624 pp.Suche in Google Scholar

[3] Anashin V. S., “Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers”, J. of Math. Sci., 89:4 (1998), 1355–1390.10.1007/BF02355442Suche in Google Scholar

[4] Blum L., Blum M., Shub M., “Comparison of two pseudo-random number generators”, Adv. in Cryptology, CRYPTO’82, N.-Y.: Plenum Press, 1983, 61–78.10.1007/978-1-4757-0602-4_6Suche in Google Scholar

[5] Eichenauer J., Lehn J., “A non-linear congruential pseudo random number generator”, Stat. Hefte, 27:1 (1986), 315–326.10.1007/BF02932576Suche in Google Scholar

[6] Eichenauer J., Lehn J., “On the structure of quadratic congruential sequences”, Manuscripta Math, 58:1–2 (1987), 129–140.10.1007/BF01169087Suche in Google Scholar

[7] Eichenauer J., Lehn J., Topuzoglu A., “A nonlinear congruential pseudorandom number generator with power of two modulus”, Math. Comput., 51:184 (1988), 757–759.10.1090/S0025-5718-1988-0958641-1Suche in Google Scholar

[8] Eichenauer J., Topuzoglu A., “On the period length of congruential pseudorandom number sequences generated by inversions”, J. Comput. Appl. Math., 31:1 (1990), 87–96.10.1016/0377-0427(90)90339-2Suche in Google Scholar

[9] Eichenauer J., “Inversive congruential pseudorandom numbers: a tutorial”, Int. Statist. Rev., 60 (1992), 167–176.10.2307/1403647Suche in Google Scholar

[10] Eichenauer J., “On generalized inversive congruential pseudorandom numbers”, Math. Comp., 63:207 (1994), 293–299.10.1090/S0025-5718-1994-1242056-8Suche in Google Scholar

[11] Heat D., Sanchez P., “On the adequacy of pseudorandom number generators (or: how big a period do we need?)”, Oper. Res. Lett., 5:1 (1986), 3–6.10.1016/0167-6377(86)90092-1Suche in Google Scholar

[12] Hill G.W., “Cyclic properties of pseudo-random sequences of Mersenne prime residues”, Comp. J., 22:1 (1979), 80–85.10.1093/comjnl/22.1.80Suche in Google Scholar

[13] Kato T., Wu L.-M., Yanagihara N., “On a nonlinear congruential pseudorandom number generator”, Math. Comput., 65:213 (1996), 227–233.10.1090/S0025-5718-96-00694-1Suche in Google Scholar

[14] Keller G., Olson F. R., “Counting polynomial functions (mod pⁿ)”, Duke Math. J., 35:4 (1968), 835–838.10.1215/S0012-7094-68-03589-8Suche in Google Scholar

[15] Niederreiter H., “Nonlinear methods for pseudorandom number and vector generation”, Simulation and Optimization. Lect. Notes Econ. Math. Systems, 374, Berlin, 1992, 145–153.10.1007/978-3-642-48914-3_11Suche in Google Scholar

[16] Niederreiter H., Random number generation and quasi-Monte Carlo methods, SIAM, Philadelphia, USA, 1992, 242 pp.10.1137/1.9781611970081Suche in Google Scholar

[17] Singmaster D., “On polynomial functions (mod m)”, J. Numb. Theory, 6:5 (1974), 345–352.10.1016/0022-314X(74)90031-6Suche in Google Scholar

[18] Sachkov V. N, An introduction to Combinatorial Methods of Discrete Mathematics, Nauka, M., 1982 (in Russian), 384 pp.Suche in Google Scholar

[19] McDonald B. R., Finite rings with identity, Marcel Dekker Inc., 1974, 448 pp.Suche in Google Scholar

[20] Elizarov V.P., Finite rings, M.: Gelios ARV, 2006 (in Russian), 304 pp.Suche in Google Scholar

[21] Melihov A.N., Directed graphs and finite automata, Nauka, M.:, 1971 (in Russian), 416 pp.Suche in Google Scholar

[22] Gill A., Linear Sequential Circuits, McGraw-Hill, N.-Y., 1967, 215 pp.Suche in Google Scholar

[23] Wang K. C., “Transition graphs of affine transformation on vector spaces over finite fields”, J. Franklin Inst., 283:1 (1967), 55–72.10.1016/0016-0032(67)90115-9Suche in Google Scholar

[24] Nechaev A. A., “Cycle types of linear substitutions over finite commutative rings”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 283–311.10.1070/SM1994v078n02ABEH003470Suche in Google Scholar

[25] Lidl R., Niederreiter H., Finite Fields, CUP, Cambridge, 1997, 755 pp.10.1017/CBO9780511525926Suche in Google Scholar

[26] Kostrikin A. I., Introduction to algebra, Springer-Verlag, 1982, 575 pp.10.1007/978-1-4615-7286-2Suche in Google Scholar

[27] Ermilov D. M., Kozlitin O. A., “The cycle structure of a polynomial generator over the Galois ring”, Matem. vopr. kriptogr., 4:1 (2013), 27–57 (in Russian).10.4213/mvk72Suche in Google Scholar

[28] Nechaev A. A., “Polynomial transformations of finite commutative local rings of principal ideals”, Math. Notes, 27:6 (1980), 425–432.10.1007/BF01145430Suche in Google Scholar