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A NEW PROOF OF THE CARLITZ–LUTZ THEOREM
Published online by Cambridge University Press: 10 July 2019
Abstract
A polynomial $f$ over a finite field $\mathbb{F}_{q}$ can be classified as a permutation polynomial by the Hermite–Dickson criterion, which consists of conditions on the powers $f^{e}$ for each $e$ from $1$ to $q-2$, as well as the existence of a unique solution to $f(x)=0$ in $\mathbb{F}_{q}$. Carlitz and Lutz gave a variant of the criterion. In this paper, we provide an alternate proof to the theorem of Carlitz and Lutz.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 56 - 60
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
The second and third authors were supported by NSERC.