On properties of output sequence of multi-cyclic generator over direct sum of residue groups modulo~2
Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 45-53.

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

The formula for the frequencies of symbols in the output sequence of multi-cyclic generator over the direct sum of residue groups modulo 2 is obtained. In the case when cells of registers contain independent random values with the uniform distribution the limit joint distribution of the frequencies (as lengths of the registers tend to infinity) is obtained.
Keywords: multi-cyclic generator (MCV-generator), direct sum of groups of residues modulo 2, random multi-cyclic sequence, frequencies of values.
@article{DM_2017_29_3_a3,
     author = {N. M. Mezhennaya and V. G. Mikhailov},
     title = {On properties of output sequence of multi-cyclic generator over direct sum of residue groups modulo~2},
     journal = {Diskretnaya Matematika},
     pages = {45--53},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_3_a3/}
}
TY  - JOUR
AU  - N. M. Mezhennaya
AU  - V. G. Mikhailov
TI  - On properties of output sequence of multi-cyclic generator over direct sum of residue groups modulo~2
JO  - Diskretnaya Matematika
PY  - 2017
SP  - 45
EP  - 53
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2017_29_3_a3/
LA  - ru
ID  - DM_2017_29_3_a3
ER  - 
%0 Journal Article
%A N. M. Mezhennaya
%A V. G. Mikhailov
%T On properties of output sequence of multi-cyclic generator over direct sum of residue groups modulo~2
%J Diskretnaya Matematika
%D 2017
%P 45-53
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2017_29_3_a3/
%G ru
%F DM_2017_29_3_a3
N. M. Mezhennaya; V. G. Mikhailov. On properties of output sequence of multi-cyclic generator over direct sum of residue groups modulo~2. Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 45-53. http://geodesic.mathdoc.fr/item/DM_2017_29_3_a3/

[1] Pohl P., “The multicyclic vector method of generating pseudo-random numbers. I. Theoretical background, description of the method and algebraic analysis”, Report TRITA-NA-7307, 1973, Royal Inst. of Technology, Stockholm, Sweden, 36 pp.

[2] Pohl P., “Description of MCV, a pseudo–random number generator”, Scand. Actuarial J., 1 (1976), 1–14 | DOI | MR | Zbl

[3] Mezhennaya N. M., Mikhailov V. G., “O raspredelenii chisla edinits v vykhodnoi posledovatelnosti generatora Pola nad polem $GF(2)$”, Matematicheskie voprosy kriptografii, 4:4 (2013), 95—107

[4] Mezhennaya N. M., “Convergence rate estimators for the number of ones in outcome sequence of MCV generator with m-dependent registers items”, Siberian Electronic Mathematical Reports, 11 (2014), 18–25 | MR | Zbl

[5] Mezhennaya N. M., “O raspredelenii chisla edinits v dvoichnoi multitsiklicheskoi posledovatelnosti”, Prikl. diskr. matem., 2015, no. 1(27), 69–77

[6] Mezhennaya N. M., Mikhailov V. G., “On frequencies of elements in multicyclic random sequence modulo 4”, Discrete Math. Appl., 25:6 (2015), 359–365 | DOI | DOI | MR | Zbl

[7] Mezhennaya N. M., Mikhailov V. G., “Ob asimptoticheskoi normalnosti chisel poyavlenii znakov v neravnoveroyatnoi multitsiklicheskoi sluchainoi posledovatelnosti po modulyu 4”, Matematicheskie voprosy kriptografii, 7:4 (2016), 81-94 | MR

[8] Hasse H., Vorlesungen