Geodesic
Periodic properties of a~simplest 2-linear shift register
Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 51-78

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The state transition graph of a simplest self-controlled 2-linear shift register over Galois ring $R=GR(2^{rn},2^n)$ is studied. An upper bound for the length of a cycle in this graph is obtained. In the case $R=\mathbf Z_{2^n}$, states belonging to cycles of maximal length are described and the number of these states is evaluated. 
@article{DM_2007_19_3_a4,
     author = {O. A. Kozlitin},
     title = {Periodic properties of a~simplest 2-linear shift register},
     journal = {Diskretnaya Matematika},
     pages = {51--78},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2007_19_3_a4/}
}
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O. A. Kozlitin. Periodic properties of a~simplest 2-linear shift register. Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 51-78. http://geodesic.mathdoc.fr/item/DM_2007_19_3_a4/