Guardat en:
| Autors principals: | , |
|---|---|
| Format: | Preprint |
| Publicat: |
2009
|
| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/0903.2016 |
| Etiquetes: |
Afegir etiqueta
Sense etiquetes, Sigues el primer a etiquetar aquest registre!
|
Taula de continguts:
- We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer $t\geq 3$ is said to be exceptional if $f(x)=x^t$ is APN (Almost Perfect Nonlinear) over $\mathbb{F}_{2^n}$ for infinitely many values of $n$. Equivalently, $t$ is exceptional if the binary cyclic code of length $2^n-1$ with two zeros $ω, ω^t$ has minimum distance 5 for infinitely many values of $n$. The conjecture we prove states that every exceptional number has the form $2^i+1$ or $4^i-2^i+1$.