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Mat. Vopr. Kriptogr., 2014, Volume 5, Issue 2, Pages 57–70 (Mi mvk117)  

This article is cited in 1 scientific paper (total in 1 paper)

Description of maximal skew linear recurrences in terms of multipliers

S. N. Zaitsev

LLC "Certification Research Center", Moscow

Abstract: Let $P=\mathrm{GF}(q)$ be a field, $F=\mathrm{GF}(q^n)$ be an extension of $P$. We construct a wide class of skew MP-polynomials over $F$ by the description of multipliers of skew MP LRS. For $P$-skew MP LRS $v$ over $F$ we call linear transformation $\psi$ (generalized) multiplier if there exists a number $l\geq0$ such that $\psi(v(i))=v(i+l)$, $i\geq0$. Denote by $\mathfrak M(v)^*$ the set of all multipliers of a skew MP LRS $v$, and $\mathfrak M(v)=\mathfrak M(v)^*\cup\{0\}$. It is proved that $\mathfrak M(v)$ is a field and $\mathfrak M(v)\cong F$ if and only if $v$ is linearized. Sufficient conditions for $\mathfrak M(v)\cong P$ are given. It is proved that for any $P$-skew MP LRS $v$ there exists a transformation $\psi$ such that the sequence $\psi(v)$ is $\mathfrak M(v)$-skew MP LRS of the same order, and for any field $K<F$ there exists MP LRS $v$ such that $\mathfrak M(v)\cong K$.

Key words: skew linear recurrence, skew polynomial of maximal period, generalized multiplier, maximal non-reducible sequence.

DOI: https://doi.org/10.4213/mvk117

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UDC: 519.624+519.113.6
Received 25.IX.2013
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Citation: S. N. Zaitsev, “Description of maximal skew linear recurrences in terms of multipliers”, Mat. Vopr. Kriptogr., 5:2 (2014), 57–70

Citation in format AMSBIB
\Bibitem{Zai14}
\by S.~N.~Zaitsev
\paper Description of maximal skew linear recurrences in terms of multipliers
\jour Mat. Vopr. Kriptogr.
\yr 2014
\vol 5
\issue 2
\pages 57--70
\mathnet{http://mi.mathnet.ru/mvk117}
\crossref{https://doi.org/10.4213/mvk117}


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    This publication is cited in the following articles:
    1. S. N. Zaitsev, “A triangular class of skew maximum-period polynomials”, Problems Inform. Transmission, 52:4 (2016), 391–399  mathnet  crossref  isi  elib
  • Математические вопросы криптографии
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