Geodesic
The second coordinate sequence of a linear recurrence of maximum period over ring $\mathbb{Z}_{8}$
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 9-10 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The analytical structure of the second coordinate in a linear recurrence sequence over ring $\mathbb{Z}_{8}$ is described. The lower bound of its rank (linear complexity) is specified. The class of polynomials and recurrences of the maximum period with the highest possible rank is found.
Keywords: linear recurring sequence, coordinate sequence, rank, analytical structure. 
@article{PDMA_2013_6_a2,
     author = {D. N. Bylkov},
     title = {The second coordinate sequence of a linear recurrence of maximum period over ring $\mathbb{Z}_{8}$},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {9--10},
     year = {2013},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a2/}
}
TY  - JOUR
AU  - D. N. Bylkov
TI  - The second coordinate sequence of a linear recurrence of maximum period over ring $\mathbb{Z}_{8}$
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2013
SP  - 9
EP  - 10
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/PDMA_2013_6_a2/
LA  - ru
ID  - PDMA_2013_6_a2
ER  - 
%0 Journal Article
%A D. N. Bylkov
%T The second coordinate sequence of a linear recurrence of maximum period over ring $\mathbb{Z}_{8}$
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2013
%P 9-10
%N 6
%U http://geodesic.mathdoc.fr/item/PDMA_2013_6_a2/
%G ru
%F PDMA_2013_6_a2
D. N. Bylkov. The second coordinate sequence of a linear recurrence of maximum period over ring $\mathbb{Z}_{8}$. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 9-10. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a2/

[1] Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear Recurring Sequences over Rings and Modules”, J. Math. Sci. (New York), 76:6 (1995), 2793–2915 | DOI | MR

[2] Helleseth T., Martinsen H. M., “Binary sequences of period $2^m-1$ with large linear complexity”, Information and Computation, 151 (1999), 73–91 | DOI | MR

[3] Kurakin V. L., “Pervaya koordinatnaya posledovatelnost lineinoi rekurrenty maksimalnogo perioda nad koltsom Galua”, Diskretnaya matematika, 6:2 (1994), 88–100