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 Mat. Vopr. Kriptogr., 2014, Volume 5, Issue 2, Pages 37–46 (Mi mvk115)

A construction of skew LRS of maximal period over finite fields based on the defining tuples of factors

M. A. Goltvanitsa

LLC "Certification Research Center", Moscow

Abstract: Let $p$ be a prime number, $R=\mathrm{GF}(q)$ be a field of $q=p^r$ elements and $S=\mathrm{GF}(q^n)$ be an extension of $R$. Let $\breve S$ be the ring of all linear transformations of the space $_RS$. A linear recurrent sequence $v$ of order $m$ over the module $_{\breve S}S$ is said to be a skew linear recurrence sequence (skew LRS) of order $m$ over $S$. The period $T(v)$ of such sequence satisfies the inequality $T(v)\leq\tau=q^{mn}-1$. If $T(v)=\tau$ we call $v$skew LRS of maximal period (skew MP LRS). Here new classes of skew MP LRS based on the notion of the defining tuples of factors are constructed.

Key words: finite field, skew linear recurrence of maximal period.

DOI: https://doi.org/10.4213/mvk115

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Citation: M. A. Goltvanitsa, “A construction of skew LRS of maximal period over finite fields based on the defining tuples of factors”, Mat. Vopr. Kriptogr., 5:2 (2014), 37–46

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\Bibitem{Gol14} \by M.~A.~Goltvanitsa \paper A construction of skew LRS of maximal period over finite fields based on the defining tuples of factors \jour Mat. Vopr. Kriptogr. \yr 2014 \vol 5 \issue 2 \pages 37--46 \mathnet{http://mi.mathnet.ru/mvk115} \crossref{https://doi.org/10.4213/mvk115} 

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• https://doi.org/10.4213/mvk115
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This publication is cited in the following articles:
1. M. A. Goltvanitsa, “Non-commutative Hamilton–Cayley theorem and roots of characteristic polynomials of skew maximal period linear recurrences over Galois rings”, Matem. vopr. kriptogr., 8:2 (2017), 65–76
2. M. A. Goltvanitsa, “Equidistant filters based on skew ML-sequences over fields”, Matem. vopr. kriptogr., 9:2 (2018), 71–86
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