Geodesic
On the minimal coset covering for a special subset in direct product of two finite fields
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 3, pp. 236-240

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In this paper we estimate the minimal number of systems of linear equations of $n+m$ variables over a finite field $F_q$ such that the union of all solutions of all the systems coincides exactly with all elements of $\overset{\ast}{\mathbb{F}_{q}^{n}} \times \overset{\ast}{\mathbb{F}_{q}^{m}}$
Keywords: linear algebra, covering with cosets. 
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A. V. Minasyan. On the minimal coset covering for a special subset in direct product of two finite fields. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 3, pp. 236-240. http://geodesic.mathdoc.fr/item/UZERU_2017_51_3_a4/