Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On existence of primitive normal elements of rational form over finite fields of even characteristic (2005.01216v3)

Published 4 May 2020 in math.NT

Abstract: Let $q$ be an even prime power and $m\geq2$ an integer. By $\mathbb{F}q$, we denote the finite field of order $q$ and by $\mathbb{F}{qm}$ its extension degree $m$. In this paper we investigate the existence of a primitive normal pair $(\alpha, \, f(\alpha))$, with $f(x)= \dfrac{ax2+bx+c}{dx+e} \in \mathbb{F}{qm}(x)$, where the rank of the matrix $F= \begin{pmatrix}a \, &b\, & c\ 0\, &d \, &e \end{pmatrix}$ $\in M{2 \times 3}(\Fm) $ is 2. Namely, we establish sufficient conditions to show that nearly all fields of even characteristic possess such elements, except for $\begin{pmatrix} 1 \, &1 \, & 0\ 0\, &1 \, &0 \end{pmatrix}$ if $q=2$ and $m$ is odd, and then we provide an explicit list of possible and genuine exceptional pairs $(q,m)$.

Summary

We haven't generated a summary for this paper yet.