Geodesic
Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings
Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 57-68.

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We study the frequencies of tuples in linear recurring sequences (LRS) of vectors over Galois rings. By means of an estimate of an exponential sum some nontrivial bounds on the frequencies of elements in LRS are derived. It is shown that these bounds are in some cases sharper than known results.
Keywords: linear recurring sequences, Galois ring, distribution of elements in a sequence, exponential sums. 
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A. R. Vasin. Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings. Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 57-68. http://geodesic.mathdoc.fr/item/DM_2019_31_2_a4/

[1] V.L. Kurakin, A.S. Kuzmin, A.V. Mikhalev, A.A. Nechaev, “Linear recurring sequences over rings and modules”, J. Math. Sci., 76:6 (1995), 2793–2915 | DOI | MR | Zbl

[2] A.S. Kuzmin, V.L. Kurakin, A.A. Nechaev, “Psevdosluchainye i polilineinye posledovatelnosti”, Trudy po diskretnoi matematike, 1, Izd-vo TVP, M., 1997, 139-202

[3] O.V. Kamlovskii, “Frequency characteristics of coordinate sequences of linear recurrences over Galois rings”, Izv. Math., 77:6 (2013), 1130–1154 | DOI | DOI | MR | Zbl

[4] O.V. Kamlovskii, “The Sidel’nikov method for estimating the number of signs on segments of linear recurrence sequences over Galois rings”, Math. Notes, 91:3 (2012), 354–363 | DOI | DOI | MR | Zbl

[5] M.M. Glukhov, “Primenenie metoda Niderraitera-Shparlinskogo otsenki nepolnykh trigonometricheskikh summ k summam nad koltsami Galua”, Algebra i logika: teoriya i prilozheniya, Mezhdunarodnaya konferentsiya, posvyaschennaya pamyati V.P. Shunkova (Krasnoyarsk, 21-27 iyulya 2013), 37-39

[6] A.A. Nechaev, “Kerdock code in a cyclic form”, Discrete Math. Appl., 1:4 (1991), 365–384 | DOI | MR | Zbl | Zbl

[7] B.R. McDonald, Finite rings with identity, Pure Appl. Math., 28, Dekker, New York, 1974, 429 pp. | MR | Zbl

[8] A.A. Nechaev, “Cycle types of linear substitutions over finite commutative rings”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 283–311 | DOI | MR | Zbl

[9] H. Niederreiter, I.E. Shparlinski, “On the distribution and lattice structure of nonlinear congruential pseudorandom numbers”, Finite Fields Appl., 5 (1999), 246-253 | DOI | MR | Zbl

[10] P. Sole, D. Zinoviev, “Inversive congruential pseudorandom numbers over Galois rings”, Eur. J. Comb., 30:2 (2009), 458-467 | DOI | MR | Zbl

[11] E. V. Vernigora, “Inversive congruential generator over a Galois ring of dimension $p^l$”, J. Math. Sci., 182:1 (2012), 108-116 | DOI | MR | Zbl

[12] O. V. Kamlovskii, A. S. Kuzmin, “Otsenki chastot poyavleniya elementov v lineinykh rekurrentnykh posledovatelnostyakh nad koltsami Galua”, Fund. i prikl. matem., 6:4 (2000), 1083–1094 | MR | Zbl

[13] O.V. Kamlovskii, “Frequency characteristics of linear recurrence sequences over Galois rings”, Sb. Math., 200:4 (2009), 499–519 | DOI | DOI | MR | Zbl | Zbl