ON LINEARIZED COVERINGS OF A CUBIC HOMOGENEOUS EQUATION OVER A FINITE FIELD. LOWER BOUNDS

V.P. Gabrielyan

doi:10.46991/PYSU:A/2019.53.2.119

ON LINEARIZED COVERINGS OF A CUBIC HOMOGENEOUS EQUATION OVER A FINITE FIELD. LOWER BOUNDS

Authors

V.P. Gabrielyan Chair of Discrete Mathematics and Theoretical Informatics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2019.53.2.119

Keywords:

linear algebra, finite field, coset of linear subspace, linearized covering

Abstract

We obtain lower bounds for the complexity of linearized coverings for some sets of special solutions of the equation $$ x_{1}x_{2}x_{3} \mathclose{+} x_{2}x_{3}x_{4} \mathclose{+} \cdots \mathclose{+} x_{3n}x_{1}x_{2} \mathclose{+} x_{1}x_{3}x_{5} \mathclose{+} x_{4}x_{6}x_{8} \mathclose{+} \cdots \mathclose{+} x_{3n-2}x_{3n}x_{2} \mathclose{=} b $$ over an arbitrary finite field.

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Published

2019-08-15

How to Cite

Gabrielyan, V. (2019). ON LINEARIZED COVERINGS OF A CUBIC HOMOGENEOUS EQUATION OVER A FINITE FIELD. LOWER BOUNDS. Proceedings of the YSU A: Physical and Mathematical Sciences, 53(2 (249), 119–126. https://doi.org/10.46991/PYSU:A/2019.53.2.119