Geodesic
An algorithm to restore a linear recurring sequence over the ring $R=\mathbf Z_{p^n}$ from a linear complication of its highest coordinate sequence
Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 104-120
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $u$ be a linear recurring sequence of maximal period over the ring $\mathbf Z_{p^n}$ and be a pseudo-random sequence over the field $\mathbf Z_p$ obtained by multiplying the highest coordinate sequence of $u$ by some polynomial. In this paper we analyse possibilities and ways to restore $u$ from a given $v$. A short survey of earlier results is given. 
@article{DM_2010_22_4_a7,
     author = {D. N. Bylkov and A. A. Nechaev},
     title = {An algorithm to restore a~linear recurring sequence over the ring $R=\mathbf Z_{p^n}$ from a~linear complication of its highest coordinate sequence},
     journal = {Diskretnaya Matematika},
     pages = {104--120},
     year = {2010},
     volume = {22},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_4_a7/}
}
TY  - JOUR
AU  - D. N. Bylkov
AU  - A. A. Nechaev
TI  - An algorithm to restore a linear recurring sequence over the ring $R=\mathbf Z_{p^n}$ from a linear complication of its highest coordinate sequence
JO  - Diskretnaya Matematika
PY  - 2010
SP  - 104
EP  - 120
VL  - 22
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/DM_2010_22_4_a7/
LA  - ru
ID  - DM_2010_22_4_a7
ER  - 
%0 Journal Article
%A D. N. Bylkov
%A A. A. Nechaev
%T An algorithm to restore a linear recurring sequence over the ring $R=\mathbf Z_{p^n}$ from a linear complication of its highest coordinate sequence
%J Diskretnaya Matematika
%D 2010
%P 104-120
%V 22
%N 4
%U http://geodesic.mathdoc.fr/item/DM_2010_22_4_a7/
%G ru
%F DM_2010_22_4_a7
D. N. Bylkov; A. A. Nechaev. An algorithm to restore a linear recurring sequence over the ring $R=\mathbf Z_{p^n}$ from a linear complication of its highest coordinate sequence. Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 104-120. http://geodesic.mathdoc.fr/item/DM_2010_22_4_a7/

[1] 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

[2] Kuzmin A. S., Kurakin V. L., Nechaev A. A., “Koltsa Galua v prilozheniyakh k kodam i rekurrentam”, Trudy Akademii kriptografii RF, Nauka, Moskva, 1998 | Zbl

[3] Kuzmin A. S., Nechaev A. A., “Lineinye rekurrentnye posledovatelnosti nad koltsami Galua”, Uspekhi matem. nauk, 48:1 (1993), 167–168 | MR | Zbl

[4] Kuzmin A. S., Nechaev A. A., “Lineinye rekurrentnye posledovatelnosti nad koltsami Galua”, Algebra i logika, 34:2 (1995), 169–189 | MR

[5] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, Moskva, 2004

[6] Tian Tian, Wen-Feng Qi, “Injectivity of compressing map on primitive sequences over $\mathbb Z_{p^l}$”, IEEE Trans. Inform. Theory, 53:8 (2007), 2960–2966 | DOI | MR

[7] Xuan-Yong Zhu, Wen-Feng Qi, “Uniqueness of the distribution of zeros of primitive level sequences over $\mathbb Z_{p^n}$”, Finite Fields Appl., 11:1 (2005), 30–44 | DOI | MR | Zbl

[8] Xuan-Yong Zhu, Wen-Feng Qi, “Compression mappings on primitive sequences over $\mathbb Z_{p^n}$”, IEEE Trans. Inform. Theory, 50:10 (2004), 2442–2448 | DOI | MR

[9] Xuan-Yong Zhu, Wen-Feng Qi, “Further results of compressing maps on primitive sequences over $\mathbb Z_{p^n}$”, Math. Comp., 77 (2008), 1623–1637 | DOI | MR | Zbl

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