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