Geodesic
An upper bound for the complexity of linearized coverings in a finite field
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2010), pp. 41-48.

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

The minimal number of systems of linear equations with $n$ unknowns over a finite field $F_q$, such that the union of all solutions of the systems forms an exact cover for a given subset in $F_q^n$, is the complexity of a linearized covering. An upper bound for the complexity for “almost all” subsets in $F_q^n$ is presented. 
@article{UZERU_2010_2_a6,
     author = {H. K. Nurijanyan},
     title = {An upper bound for the complexity of linearized coverings in a finite field},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {41--48},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2010_2_a6/}
}
TY  - JOUR
AU  - H. K. Nurijanyan
TI  - An upper bound for the complexity of linearized coverings in a finite field
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2010
SP  - 41
EP  - 48
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2010_2_a6/
LA  - en
ID  - UZERU_2010_2_a6
ER  - 
%0 Journal Article
%A H. K. Nurijanyan
%T An upper bound for the complexity of linearized coverings in a finite field
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2010
%P 41-48
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2010_2_a6/
%G en
%F UZERU_2010_2_a6
H. K. Nurijanyan. An upper bound for the complexity of linearized coverings in a finite field. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2010), pp. 41-48. http://geodesic.mathdoc.fr/item/UZERU_2010_2_a6/

[1] A. Alexanian, Disjunctive Normal Forms Over Linear Functions (Theory and Applications), YSU press, Yer., 1990, 201 pp. (in Russian) | MR

[2] A. Alexanian, “Realization of Boolean functions by disjunctions of products of linear forms”, Soviet. Mat. Dokl., 39:1 (1989), 131–135 (in Russian) | MR

[3] V. Gabrielian, On Metric Characterization Connected with Covering Subset of Finite Fields by Cosets of the Linear Subspaces, Institut Problem Informatiki i Avtomatizacii, Yer., 2004 (in Russian)

[4] A. Andreev, “A modification of the gradient algorithm”, Vestnik Moskovskogo Universiteta, 1985, no. 3, 29–35 (in Russian) | MR | Zbl