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JOURNALS // Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography] // Archive

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

This article is cited in 6 papers

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.

UDC: 519.624+519.113.6

Received 25.IX.2013

Language: English

DOI: 10.4213/mvk115



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