Recovery of a~polynomially complicated linear recurring sequence over Galois ring by its senior coordinate
Prikladnaâ diskretnaâ matematika, no. 2 (2014), pp. 21-36.

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

Maximal peroid linear recurring sequences (LRS) over a Galois ring, which are complicated with a polynomial over this ring, are considered. An algorithm is proposed for recovering the initial vector of a LRS by the senior coordinate of its complicated sequence.
Keywords: LRS of maximal period, complicated polynomial, senior coordinate sequence, recovery of initial vector.
@article{PDM_2014_2_a2,
     author = {E. M. Serebryakov},
     title = {Recovery of a~polynomially complicated linear recurring sequence over {Galois} ring by its senior coordinate},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {21--36},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_2_a2/}
}
TY  - JOUR
AU  - E. M. Serebryakov
TI  - Recovery of a~polynomially complicated linear recurring sequence over Galois ring by its senior coordinate
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 21
EP  - 36
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_2_a2/
LA  - ru
ID  - PDM_2014_2_a2
ER  - 
%0 Journal Article
%A E. M. Serebryakov
%T Recovery of a~polynomially complicated linear recurring sequence over Galois ring by its senior coordinate
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 21-36
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2014_2_a2/
%G ru
%F PDM_2014_2_a2
E. M. Serebryakov. Recovery of a~polynomially complicated linear recurring sequence over Galois ring by its senior coordinate. Prikladnaâ diskretnaâ matematika, no. 2 (2014), pp. 21-36. http://geodesic.mathdoc.fr/item/PDM_2014_2_a2/

[1] Kuzmin A. S., Marshalko G. B., Nechaev A. A., “Vosstanovlenie lineinoi rekurrenty nad primarnym koltsom vychetov po eë uslozhneniyu”, Matematicheskie voprosy kriptografii, 1:2 (2010), 31–56

[2] Bylkov D. N., “Klass uslozhnenii lineinykh rekurrent nad koltsom Galua, ne privodyaschii k potere informatsii”, Problemy peredachi informatsii, 46:3 (2010), 51–59 | MR | Zbl

[3] Tian T., Wen-Feng Q., “Injectivity of compressing map on primitive sequences over $\mathbb Z/(p^e)$”, IEEE Trans. Inform. Theory, 53:8 (2007), 2960–2966 | DOI | MR

[4] Xuan-Yong Z., Wen-Feng Q., “Uniqueness of the distribution of zeros of primitive level sequences over $\mathbb Z/(p^e)$”, Finite Fields Their Appl., 11:1 (2005), 30–44 | DOI | MR | Zbl

[5] Xuan-Yong Z., Wen-Feng Q., “Compression mappings on primitive sequences over $\mathbb Z/(p^e)$”, IEEE Trans. Inform. Theory, 50:10 (2004), 2442–2448 | DOI | MR

[6] Xuan-Yong Z., Wen-Feng Q., “Further result of compressing maps on primitive sequences modulo odd prime powers”, IEEE Trans. Inform. Theory, 53:8 (2007), 2985–2990 | DOI | MR

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

[8] Kuzmin A. S., Nechaev A. A., “Lineinye rekurrentnye posledovatelnosti nad koltsami Galua”, Algebra i logika, 3:2 (1995), 169–189 | MR

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

[10] Kuzmin A. S., Nechaev A. A., “Vosstanovlenie lineinoi rekurrentnoi posledovatelnosti nad koltsom Galua po eë starshei koordinatnoi posledovatelnosti”, Diskretnaya matematika, 23:2 (2011), 3–31 | DOI | MR | Zbl

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

[12] Kurakin V. L., “Funktsiya perenosa v pervyi razryad v koltse Galua”, Diskretnaya matematika, 24:2 (2012), 21–36 | DOI | MR | Zbl

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

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