Abstract:
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.
This publication is cited in the following 4 articles:
O. A. Kozlitin, “Ispolzovanie $2$-lineinogo registra sdviga dlya vyrabotki psevdosluchainykh posledovatelnostei”, Matem. vopr. kriptogr., 5:1 (2014), 39–72
O. A. Kozlitin, “$2$-lineinyi registr sdviga nad koltsom Galua chetnoi kharakteristiki”, Matem. vopr. kriptogr., 3:2 (2012), 27–61
O. A. Kozlitin, “Parallelnaya dekompozitsiya neavtonomnykh 2-lineinykh registrov sdviga”, Matem. vopr. kriptogr., 2:3 (2011), 5–29
O. A. Kozlitin, “Properties of the output sequence of a simplest 2-linear shift register over $\mathbf Z_{2^n}$”, Discrete Math. Appl., 17:6 (2007), 539–566