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Mat. Sb., 2009, Volume 200, Number 4, Pages 31–52 (Mi msb4528)  

This article is cited in 13 scientific papers (total in 13 papers)

Frequency characteristics of linear recurrence sequences over Galois rings

O. V. Kamlovskii

Abstract: The frequencies of occurrences of elements in linear recurrence sequences of vectors over Galois rings are studied. The study of these frequencies is reduced to the study of the corresponding trigonometric sums over Galois rings. Based on estimates for trigonometric sums, nontrivial estimates for the frequencies of occurrence of elements in linear recurrence sequences are obtained, which generalize some known results for sequences over a finite field. These estimates are asymptotically best possible.
Bibliography: 25 titles.

Keywords: linear recurrence sequences, Galois rings, trigonometric sums, distribution of elements of pseudorandom sequences, estimates for trigonometric sums.


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English version:
Sbornik: Mathematics, 2009, 200:4, 499–519

Bibliographic databases:

UDC: 519.4
MSC: Primary 11B37; Secondary 11B50, 11L03, 94A55
Received: 28.02.2008 and 23.12.2008

Citation: O. V. Kamlovskii, “Frequency characteristics of linear recurrence sequences over Galois rings”, Mat. Sb., 200:4 (2009), 31–52; Sb. Math., 200:4 (2009), 499–519

Citation in format AMSBIB
\by O.~V.~Kamlovskii
\paper Frequency characteristics of linear recurrence sequences over Galois rings
\jour Mat. Sb.
\yr 2009
\vol 200
\issue 4
\pages 31--52
\jour Sb. Math.
\yr 2009
\vol 200
\issue 4
\pages 499--519

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    This publication is cited in the following articles:
    1. O. V. Kamlovskii, “Metod trigonometricheskikh summ dlya issledovaniya chastot $r$-gramm v starshikh koordinatnykh posledovatelnostyakh lineinykh rekurrent nad koltsom $\mathbb{Z}_{2^n}$”, Matem. vopr. kriptogr., 1:4 (2010), 33–62  mathnet  crossref
    2. O. V. Kamlovskii, “The Sidelnikov Method for Estimating the Number of Signs on Segments of Linear Recurrence Sequences over Galois Rings”, Math. Notes, 91:3 (2012), 354–363  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. D. N. Bylkov, O. V. Kamlovskii, “Parametry bulevykh funktsii, postroennykh s ispolzovaniem starshikh koordinatnykh posledovatelnostei lineinykh rekurrent”, Matem. vopr. kriptogr., 3:4 (2012), 25–53  mathnet  crossref
    4. O. V. Kamlovskii, “Improved bounds for the number of occurrences of elements in linear recurrence sequences over Galois rings”, J. Math. Sci., 197:4 (2014), 512–524  mathnet  crossref
    5. Zheng Q.-X., Qi W.-F., Tian T., “On the Distinctness of Binary Sequences Derived From Primitive Sequences Modulo Square-Free Odd Integers”, IEEE Trans. Inf. Theory, 59:1 (2013), 680–690  crossref  mathscinet  zmath  isi  scopus
    6. O. V. Kamlovskii, “Frequency characteristics of coordinate sequences of linear recurrences over Galois rings”, Izv. Math., 77:6 (2013), 1130–1154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. O. V. Kamlovskii, “Kolichestvo razlichnykh multigramm v lineinykh rekurrentnykh posledovatelnostyakh nad koltsami Galua”, Matem. vopr. kriptogr., 4:3 (2013), 49–82  mathnet  crossref
    8. O. V. Kamlovskii, “Distribution of $r$-tuples in one class of uniformly distributed sequences over residue rings”, Problems Inform. Transmission, 50:1 (2014), 90–105  mathnet  crossref  isi
    9. O. V. Kamlovskii, “Svoistva raspredelenii strok i stolbtsov dlya matrichnykh lineinykh rekurrentnykh posledovatelnostei pervogo poryadka”, Matem. vopr. kriptogr., 6:4 (2015), 65–76  mathnet  crossref  mathscinet  elib
    10. O. V. Kamlovskii, “Estimating the number of solutions of systems of nonlinear equations with linear recurring arguments by the spectral method”, Discrete Math. Appl., 27:4 (2017), 199–211  mathnet  crossref  crossref  mathscinet  isi  elib
    11. A. D. Bugrov, “The cross-correlation function of complications of linear recurrent sequences”, Discrete Math. Appl., 28:2 (2018), 65–73  mathnet  crossref  crossref  mathscinet  isi  elib
    12. A. D. Bugrov, O. V. Kamlovskii, “Parametry odnogo klassa funktsii, zadannykh na konechnom pole”, Matem. vopr. kriptogr., 9:4 (2018), 31–52  mathnet  crossref  elib
    13. A. R. Vasin, “Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings”, Discrete Math. Appl., 29:5 (2019), 335–343  mathnet  crossref  crossref  isi  elib
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