ON A LINEARIZED COVERINGS OF A CUBIC HOMOGENEOUS EQUATION OVER A FINITE FIELD. UPPER BOUNDS - Gabrielyan, V.P. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2018)
We obtain upper bounds of the complexity of linearized coverings for some special solutions of the equation $$ x_{1}x_{2}x_{3} \mathclose{+} x_{2}x_{3}x_{4} \mathclose{+} … \mathclose{+} x_{3n}x_{1}x_{2} \mathclose{+} x_{1}x_{3}x_{5} \mathclose{+} x_{4}x_{6}x_{8} \mathclose{+} … \mathclose{+} x_{3n-2}x_{3n}x_{2} \mathclose{=} b $$ over an arbitrary finite field.
Keywords: linear algebra; finite field; coset of linear subspace; linearized covering