Author

Darrion Thornburgh

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Preprint Sep 2026

A new upper bound for Sidon sets in $\mathbb{F}_2^{4k+3}$

A subset $S \subseteq \mathbb{F}_2^n$ is called a Sidon set if no four distinct points of $S$ have zero sum. It is shown that if $n \geq 7$ and $n \equiv 3 \mod 4$, then $|S|\leq 2^{\frac{n+1}{2}}-3$. As a consequence, for any even $t \geq 4$, there does not exist a binary linear $[2^t-3,2^t-2t-2,5]$-code, strengthenin...

Darrion Thornburgh · 0 citations

Preprint Aug 2026

Resolving a conjecture on quadratic APN functions and a new quadratic $(n,n)$-function associated to crooked functions

We say an $(n,n)$-function $F \colon \mathbb{F}_2^n \to \mathbb{F}_2^n$ is a crooked function if for any nonzero $a \in \mathbb{F}_2^n$, the image of $D_aF(x)=F(x)+F(x+a)$ is an affine hyperplane. The only known examples of crooked functions are all quadratic almost perfect nonlinear (APN), or equivalently, for every k...

C. Carlet, Darrion Thornburgh · 1 citation · ⚡1