|
This article is cited in 9 scientific papers (total in 9 papers)
Skew LRS of maximal period over Galois rings
M. A. Goltvanitsaa, A. A. Nechaevb, S. N. Zaitseva a Moscow State Technical University of Radio Engineering, Electronics and Automatics, Moscow
b Academy of Cryptography of the Russian Federation, Moscow
Abstract:
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 $\tau=(q^{mn}-1)p^{d-1}$.
Key words:
Galois ring, Frobenius automorphism, skew linear recurrence of maximal period, skew MP-polynomial, rank of a sequence.
Received 18.IX.2012
Citation:
M. A. Goltvanitsa, A. A. Nechaev, S. N. Zaitsev, “Skew LRS of maximal period over Galois rings”, Mat. Vopr. Kriptogr., 4:2 (2013), 59–72
Linking options:
https://www.mathnet.ru/eng/mvk83https://doi.org/10.4213/mvk83 https://www.mathnet.ru/eng/mvk/v4/i2/p59
|
Statistics & downloads: |
Abstract page: | 617 | Full-text PDF : | 300 | References: | 77 |
|