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Mat. Vopr. Kriptogr., 2016, Volume 7, Issue 1, Pages 71–82 (Mi mvk175)  

This article is cited in 3 scientific papers (total in 3 papers)

On the Hamming distance between binary representations of linear recurrent sequences over field $GF(2^k)$ and ring $\mathbb{Z}_{2^n}$

O. V. Kamlovskiy

Sertification Research Center, LLC, Moscow

Abstract: Linear recurrent sequences over the field $GF(2^k)$ and over the ring $\mathbb{Z}_{2^n}$ with dependent recurrent relations are considered. We establish the bounds for the Hamming distance between two binary sequences obtained from the initial sequences by replacing each element by its image under the action of arbitrary maps into the field of two elements.

Key words: linear recurrent sequences, binary representations of sequences, finite fields, cross-correlation function.

Funding Agency Grant Number
Академия криптографии РФ


DOI: https://doi.org/10.4213/mvk175

Full text: PDF file (159 kB)
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Bibliographic databases:

UDC: 512.547+512.552
Received 20.IV.2015

Citation: O. V. Kamlovskiy, “On the Hamming distance between binary representations of linear recurrent sequences over field $GF(2^k)$ and ring $\mathbb{Z}_{2^n}$”, Mat. Vopr. Kriptogr., 7:1 (2016), 71–82

Citation in format AMSBIB
\Bibitem{Kam16}
\by O.~V.~Kamlovskiy
\paper On the Hamming distance between binary representations of linear recurrent sequences over field $GF(2^k)$ and ring $\mathbb{Z}_{2^n}$
\jour Mat. Vopr. Kriptogr.
\yr 2016
\vol 7
\issue 1
\pages 71--82
\mathnet{http://mi.mathnet.ru/mvk175}
\crossref{https://doi.org/10.4213/mvk175}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3562046}
\elib{http://elibrary.ru/item.asp?id=26475100}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. V. Kamlovskii, “Nelineinost odnogo klassa bulevykh funktsii, postroennykh s ispolzovaniem dvoichnykh razryadnykh posledovatelnostei lineinykh rekurrent nad koltsom $\mathbb Z_{2^n}$”, Matem. vopr. kriptogr., 7:3 (2016), 29–46  mathnet  crossref  mathscinet  elib
    2. 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
    3. 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
  • Математические вопросы криптографии
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