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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - O. A. Kozlitin
TI  - Periodic properties of a~simplest 2-linear shift register
JO  - Diskretnaya Matematika
PY  - 2007
SP  - 51
EP  - 78
VL  - 19
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2007_19_3_a4/
LA  - ru
ID  - DM_2007_19_3_a4
ER  - 
%0 Journal Article
%A O. A. Kozlitin
%T Periodic properties of a~simplest 2-linear shift register
%J Diskretnaya Matematika
%D 2007
%P 51-78
%V 19
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2007_19_3_a4/
%G ru
%F DM_2007_19_3_a4
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/

[1] Burbaki N., Algebra II. Moduli, koltsa, formy, Nauka, Moskva, 1966 | MR

[2] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, Gelios, Moskva, 2003

[3] Elizarov V. P., Konechnye koltsa. Osnovy teorii, Gelios, Moskva, 2006

[4] Kuzmin A. S., Kurakin V. L., Nechaev A. A., “Psevdosluchainye i polilineinye posledovatelnosti”, Trudy po diskretnoi matematike, 1 (1997), 139–202 | MR

[5] Kurakin V. L., Nechaev A. A., “Periodicheskii mnogochlen”, Entsiklopediya “Diskretnaya matematika”, Bolshaya Rossiiskaya entsiklopediya, Moskva, 2004, 201

[6] Lidl R., Niderraiter G., Konechnye polya, Mir, Moskva, 1988 | Zbl

[7] Mikhailov D. A., “Unitarnye polilineinye registry sdviga i ikh periody”, Diskretnaya matematika, 14:1 (2002), 30–59 | MR

[8] Nechaev A. A., “Mnogomernye registry sdviga i slozhnost multiposledovatelnostei”, Trudy po diskretnoi matematike, 6, 2002, 150–164

[9] Nechaev A. A., “O podobii matrits nad kommutativnym lokalnym artinovym koltsom”, Trudy seminara im. I. G. Petrovskogo, 9, 1983, 81–101 | MR | Zbl

[10] Nechaev A. A., “Tsiklovye tipy lineinykh podstanovok nad konechnymi kommutativnymi koltsami”, Matem. sb., 184:3 (1993), 21–56 | MR | Zbl

[11] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, Moskva, 1982 | MR | Zbl

[12] Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear recurring sequences over rings and modules”, J. Math. Sci., 76:6 (1995), 2793–2915 | DOI | MR | Zbl

[13] Macdonald B. R., Finite rings with identity, Marcel Dekker, New York, 1974 | MR

[14] Zsigmondy K., “Zur Theorie der Potenzreste”, Monatsh. Math. Phys., 3 (1892), 265–284 | DOI | MR