ON MINIMAL COSET COVERING OF SOLUTIONS OF A BOOLEAN EQUATION

A.V. Minasyan

doi:10.46991/PSYU:A/2015.49.1.026

ON MINIMAL COSET COVERING OF SOLUTIONS OF A BOOLEAN EQUATION

Authors

A.V. Minasyan Chair of Discrete Mathematics and Theoretical Informatics, YSU, Armenia

DOI:

https://doi.org/10.46991/PSYU:A/2015.49.1.026

Keywords:

linear algebra, covering with cosets, blocking set

Abstract

For the equation $x_1x_2\ldots x_n+x_{n+1}x_{n+2}\ldots x_{2n}+x_{2n+1}x_{2n+2}\ldots x_{3n}=1$ over the finite field $F_2$ we estimate the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the equation. We prove in this article that the number in the question is not greater than $9n^{\log_{2} 3}+4$.

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Published

2015-03-16

How to Cite

Minasyan, A. (2015). ON MINIMAL COSET COVERING OF SOLUTIONS OF A BOOLEAN EQUATION. Proceedings of the YSU A: Physical and Mathematical Sciences, 49(1 (236), 26–30. https://doi.org/10.46991/PSYU:A/2015.49.1.026