Functions of degree 4e that are not APN infinitely often

TL;DR

This paper investigates specific degree 4e polynomials and their properties related to being APN over large finite fields, providing necessary conditions and examining degree 12 cases.

Contribution

It establishes a necessary condition for degree 4e polynomials to be APN infinitely often and analyzes particular degree 12 polynomials.

Findings

Necessary condition for degree 4e polynomials to be APN infinitely often

Analysis of degree 12 polynomials in the APN context

Insights into polynomial behavior over large finite fields

Abstract

We prove a necessary condition for some polynomials of degree 4e (e an odd number) to be APN over F q n for large n, and we investigate the polynomials f of degree 12.