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Theoretical Foundations of Applied Discrete Mathematics
Exact formula for exponent of mixing digraph of feedback shift register
V. M. Fomichevabc, Ya. E. Avezovad a National Engineering Physics Institute "MEPhI", Moscow
b Financial University under the Government of the Russian Federation, Moscow
c Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
d АО «Позитив Текнолоджиз»
Abstract:
Let $g$ be a binary $n$-stage nonlinear shift register with feedback $f(x_0,\ldots,x_{n-1})$ and $\Gamma(g)$ denotes a mixing digraph of transformation $g$. By $d_m$ we denote the greatest number of essential variable of $f$.
For primitive digraph $\Gamma(g)$, we obtain the exact formulas for exponent of $\Gamma(g)$ for $d_m\in\{n-1,n-2\}$ and of
local exponents $\gamma_{u,v}$ for $0\leq u,v<n$.
Keywords:
local primitivity of digraph, mixing digraph, primitive digraph, shift register, digraph exponent.
Citation:
V. M. Fomichev, Ya. E. Avezova, “Exact formula for exponent of mixing digraph of feedback shift register”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 29–31
Linking options:
https://www.mathnet.ru/eng/pdma423 https://www.mathnet.ru/eng/pdma/y2019/i12/p29
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Abstract page: | 162 | Full-text PDF : | 38 | References: | 16 |
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