Geodesic
The Berlekamp--Massey algorithm over commutative Artinian principal ideal rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1061-1101

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

The algorithm constructing the monic polynomial of minimal degree which generates the given sequense of the length $l$ over commutative Artinian principal ideal ring $R$ is presented. The complexity of the algorithm is $O(l^2 n)$ operations of $R$, where $n$ is the index of nilpotency of the radical of $R$. The algorithm is applied for construction of the canonical system of generators of the ideal of all polynomials annihilating the given linear recurring sequence over $R$. 
@article{FPM_1999_5_4_a6,
     author = {V. L. Kurakin},
     title = {The {Berlekamp--Massey} algorithm over commutative {Artinian} principal ideal rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1061--1101},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a6/}
}
TY  - JOUR
AU  - V. L. Kurakin
TI  - The Berlekamp--Massey algorithm over commutative Artinian principal ideal rings
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1999
SP  - 1061
EP  - 1101
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a6/
LA  - ru
ID  - FPM_1999_5_4_a6
ER  - 
%0 Journal Article
%A V. L. Kurakin
%T The Berlekamp--Massey algorithm over commutative Artinian principal ideal rings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1999
%P 1061-1101
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a6/
%G ru
%F FPM_1999_5_4_a6
V. L. Kurakin. The Berlekamp--Massey algorithm over commutative Artinian principal ideal rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1061-1101. http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a6/