Christof Beierle

activity

20202025

most citedGeneralized Almost Perfect Nonlinear Binomials and Trinomials Over Fields of Prime-Square Order

2 citations · 2 across the 5 of their papers we have counts for

collaborators

10 papers

math.CO2025

Millions of inequivalent quadratic APN functions in eight variables

Christof Beierle, Philippe Langevin, Gregor Leander +2

The only known example of an almost perfect nonlinear (APN) permutation in even dimension was obtained by applying CCZ-equivalence to a specific quadratic APN function in dimension…

math.CO2024

A degree bound for planar functions

Christof Beierle, Tim Beyne

Using Stickelberger's theorem on Gauss sums, we show that if $F$ is a planar function on a finite field $F_{q}$ , then for all non-zero functions $G : \mathbb{F}_q \to \mathb…

math.RA2022

On Matrix Algebras Isomorphic to Finite Fields and Planar Dembowski-Ostrom Monomials

Christof Beierle, Patrick Felke

Let $p$ be a prime and $n$ a positive integer. As the first main result, we present a deterministic algorithm for deciding whether the matrix algebra $F_{p} [A_{1}, \dots, A_{t}]$ …

math.CO2022★ 2 cited

Generalized Almost Perfect Nonlinear Binomials and Trinomials Over Fields of Prime-Square Order

Christof Beierle

Let $p > 3$ be a prime. We show that, for each integer $d$ with $p \leq d \leq 2 (p - 1)$ , there exists a generalized almost perfect nonlinear (GAPN) binomial or trinomial over $\mathbb…

cs.IT2022

Classification of Planar Monomials Over Finite Fields of Small Order

Christof Beierle, Patrick Felke

For all finite fields of order up to $2^{30}$ , we computationally prove that there are no planar monomials besides the ones already known.

cs.IT2022

Gold Functions and Switched Cube Functions Are Not 0-Extendable in Dimension $n > 5$

Christof Beierle, Claude Carlet

In the independent works by Kalgin and Idrisova and by Beierle, Leander and Perrin, it was observed that the Gold APN functions over $F_{2^{5}}$ give rise to a quadratic APN…