On Coset Coverings of Solutions of Homogeneous Cubic Equations over Finite Fields

Abstract

Given a cubic equation $x_1y_1z_1+x_2y_2z_2+\cdots +x_ny_nz_n=b$ over a finite field, it is necessary to determine 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 initial equation. The problem is solved for arbitrary size of the field. A covering with almost minimum complexity is constructed.