Minimal value set binomials and Frobenius nonclassical curves

TL;DR

This paper characterizes minimal value set binomials over finite fields and classifies certain Frobenius nonclassical quadrinomial curves, advancing understanding of algebraic curves and binomials in finite field theory.

Contribution

It provides a complete characterization of minimal value set binomials and classifies Frobenius nonclassical quadrinomial curves with separated variables over finite fields.

Findings

All minimal value set binomials over _q are characterized.

Classification of _q-Frobenius nonclassical quadrinomial curves with separated variables.

New insights into the structure of algebraic curves over finite fields.

Abstract

In this paper, we characterize all minimal value set binomials over $\mathbb{F}_q$, that is, binomials whose size of the set of images is the smallest possible. With this information, we also classify all quadrinomial curves with separated variables that are $\mathbb{F}_q$-Frobenius nonclassical for the morphism of lines.