${\mathbb{F}}_q$-zeros of sparse trivariate polynomials and toric 3-fold codes

Kyle Meyer, Ivan Soprunov, Jenya Soprunova

For a given lattice polytope $P$ in ${\mathbb{R}}^3$, consider the space ${\mathcal{L}}_P$ of trivariate polynomials over a finite field ${\mathbb{F}}_q$, whose Newton polytopes are cont…