Geodesic
On a linearized coverings of a cubic homogeneous equation over a finite field. Lower bounds
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 119-126.

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We obtain lower bounds for the complexity of linearized coverings for some sets of special solutions of the equation $x_1 x_2 x_3+ x_2 x_3 x_4+\cdots+ x_{3n} x_1 x_2+x_1 x_3 x_5+x_4 x_6 x_8+\cdots+x_{3n-2} x_{3n}x_2=b$ over an arbitrary finite field.
Keywords: Linear algebra, finite field, coset of linear subspace, linearized covering. 
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V. P. Gabrielyan. On a linearized coverings of a cubic homogeneous equation over a finite field. Lower bounds. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 119-126. http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a5/

[1] R. Lidl, H. Niederreiter, Finite Fields, Encyclopedia Math. Appl., 20, Cambridge University Press, Cambridge, 1987 | MR | Zbl

[2] A. A. Alexanyan, “Realization of Boolean Functions by Disjunctions of Products of Linear Forms.”, Soviet Math. Dokl., 39:1 (1989), 131–135 (in Russian) | MR

[3] A. A. Alexanyan, Disjunctive Normal Forms over Linear Functions. Theory and Applications, YSU Press, Yer., 1990 (in Russian) | MR

[4] A. Alexanian, R. Serobian, “Covers Concerned with the Quadratic over Finite Field Equations”, Dokl. AN Arm. SSR, 93:1 (1992), 6–10 (in Russian) | MR

[5] V. Gabrielyan, On Metric Characteristics Associated with Coverings of Subsets of Finite Fields by Cosets of Linear Subspaces, Preprint 04-0603, Institute for Informatics and Automation Problems NAS of Armenia, Yer., 2004 (in Russian)

[6] H. K. Nurijanyan, “On the Length of the Shortest Linearized Covering for “Almost All” Subsets in Finite Field”, Reports of NAS RA, 110:1 (2010), 30–34 | MR

[7] A. Alexanian, V. Gabrielyan, “Coverings of Simmetric Subsets in Finite Fields with Cosets of Linear Subspaces”, Algebra, Geom. and their Appl., 3–4 (2004), 110–124 | MR

[8] A. Aleksanyan, M. Papikian, “On Coset Coverings of Solutions of Homogeneous Cubic Equations over Finite Fields”, The Electronic Journal of Combinatorics, 8:1 (2001), 1–9 | MR

[9] V. Gabrielyan, On the Complexity of Covering a System of Cosets of a Single Equation over a Finite Field, Preprint 04-0602, Institute for Informatics and Automation Problems NAS of Armenia, Yer., 2004 (in Russian) | MR

[10] V. P. Gabrielyan, “Linearized Coverings of One Type Equations of Higher Degree over a Finite Fields”, Reports of NAS RA, 106:2 (2006), 101–107 (in Russian) | MR

[11] V. P. Gabrielyan, “Cubical Diagonal Equation over Finite Fields of Characteristic 2”, Reports of NAS RA, 110:3 (2010), 220–227 (in Russian) | MR

[12] A. A. Alexanian, A. V. Minasyan, “An Upper Bound for the Complexity of Coset Covering of Subsets in a Finite Field”, Reports of NAS RA, 117:4 (2017), 287–291 | MR

[13] A. V. Minasyan, “On the Minimal Coset Coverings of the Set of Singular and of the Set of Nonsingular Matrices”, Proceedings of the YSU. Physical and Mathematical Sciences, 52:1 (2018), 8–11

[14] A. V. Minasyan, “On the Minimal Coset Covering for a Special Subset in Direct Product of Two Finite Fields”, Proceedings of the YSU. Physical and Mathematical Sciences, 51:3 (2017), 236–240 | MR | Zbl

[15] V. P. Gabrielyan, “On a Linearized Coverings of a Cubic Homogeneous Equation over a Finite Field. Upper Bounds”, Proceedings of the YSU. Physical and Mathematical Sciences, 52:3 (2018), 180–190