Maximal and minimal representations over the Galois ring for the linear recurrent maximal period sequence over the Galois field
Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 4, pp. 5-23
R. V. Bogonatov. Maximal and minimal representations over the Galois ring for the linear recurrent maximal period sequence over the Galois field. Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 4, pp. 5-23. http://geodesic.mathdoc.fr/item/MVK_2012_3_4_a0/
@article{MVK_2012_3_4_a0,
     author = {R. V. Bogonatov},
     title = {Maximal and minimal representations over the {Galois} ring for the linear recurrent maximal period sequence over the {Galois} field},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {5--23},
     year = {2012},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2012_3_4_a0/}
}
TY  - JOUR
AU  - R. V. Bogonatov
TI  - Maximal and minimal representations over the Galois ring for the linear recurrent maximal period sequence over the Galois field
JO  - Matematičeskie voprosy kriptografii
PY  - 2012
SP  - 5
EP  - 23
VL  - 3
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MVK_2012_3_4_a0/
LA  - ru
ID  - MVK_2012_3_4_a0
ER  - 
%0 Journal Article
%A R. V. Bogonatov
%T Maximal and minimal representations over the Galois ring for the linear recurrent maximal period sequence over the Galois field
%J Matematičeskie voprosy kriptografii
%D 2012
%P 5-23
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/MVK_2012_3_4_a0/
%G ru
%F MVK_2012_3_4_a0

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

The representations over the Galois ring of the linear recurrent maximal period sequence over the Galois field are considered. Criteria of maximality and minimality of ranks of these representations are described.

[1] Bogonatov R. V., “Predstavlenie nad koltsom Galua lineinoi rekurrentnoi posledovatelnosti nad polem Galua”, Diskretnaya matematika, 19:1 (2007), 141–157 | DOI | MR | Zbl

[2] Kurakin V. L., “Predstavleniya nad koltsom $\mathbb Z_{p^n}$ lineinoi rekurrentnoi posledovatelnosti maksimalnogo perioda nad polem $GF(p)$”, Diskretnaya matematika, 4:4 (1992), 96–116 | MR | Zbl

[3] Lidl R., Niderraiter G., Konechnye polya, Mir, M., 1988, 818 pp. | MR | Zbl

[4] Nechaev A. A., “Kod Kerdoka v tsiklicheskoi forme”, Diskretnaya matematika, 1:4 (1989), 123–139 | MR | Zbl

[5] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, M., 1982, 384 pp. | MR | Zbl