Geodesic
Skew LRS of maximal period over Galois rings
Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 2, pp. 59-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $p$ be a prime number, $R=\mathrm{GR}(q^d,p^d)$ be a Galois ring with $q^d=p^{rd}$ elements and characteristic $p^d$. Denote by $S=\mathrm{GR}(q^{nd},p^d)$ a Galois extension of the ring $R$ of dimension $n$ and by $\breve S$ the ring of all linear transformations of the module $_RS$. A sequence $v$ over the ring $S$ satisfying the recursion $\forall i\in\mathbb N_0\colon v(i+m)=\psi_{m-1}(v(i+m-1))+\dots+\psi_0(v(i))$, $\psi_0,\dots,\psi_{m-1}\in\breve S$, is called a skew LRS over $S$ with a characteristic polynomial $\Psi(x)=x^m-\sum_{t=0}^{m-1}\psi_tx^t\in\breve S[x]$. We investigate the problem of construction the polynomials $\Psi$ generating LRS $v$ with the maximal possible period $\tau=(q^{mn}-1)p^{d-1}$. 
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     title = {Skew {LRS} of maximal period over {Galois} rings},
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M. A. Goltvanitsa; A. A. Nechaev; S. N. Zaitsev. Skew LRS of maximal period over Galois rings. Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 2, pp. 59-72. http://geodesic.mathdoc.fr/item/MVK_2013_4_2_a5/

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