Abstract:
Linear recurrent sequences over the field GF(2k) and over the ring Z2n 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
Received 20.IV.2015
Bibliographic databases:
Document Type:
Article
UDC:512.547+512.552
Language: Russian
Citation:
O. V. Kamlovskiy, “On the Hamming distance between binary representations of linear recurrent sequences over field GF(2k) and ring Z2n”, Mat. Vopr. Kriptogr., 7:1 (2016), 71–82
\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://mathscinet.ams.org/mathscinet-getitem?mr=3562046}
\elib{https://elibrary.ru/item.asp?id=26475100}
Linking options:
https://www.mathnet.ru/eng/mvk175
https://doi.org/10.4213/mvk175
https://www.mathnet.ru/eng/mvk/v7/i1/p71
This publication is cited in the following 4 articles:
O. V. Kamlovskii, K. N. Pankov, “Klass diskretnykh funktsii, postroennykh po neskolkim lineinym rekurrentam nad primarnym koltsom vychetov”, Diskret. matem., 37:1 (2025), 9–21
A. D. Bugrov, O. V. Kamlovskii, “Parametry odnogo klassa funktsii, zadannykh na konechnom pole”, Matem. vopr. kriptogr., 9:4 (2018), 31–52
O. V. Kamlovskii, “Nelineinost odnogo klassa bulevykh funktsii, postroennykh s ispolzovaniem dvoichnykh razryadnykh posledovatelnostei lineinykh rekurrent nad koltsom Z2n”, Matem. vopr. kriptogr., 7:3 (2016), 29–46
A. D. Bugrov, “The cross-correlation function of complications of linear recurrent sequences”, Discrete Math. Appl., 28:2 (2018), 65–73
Citation in format AMSBIB
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