Josimar J. R. Aguirre

activity

20202025

2

-normal elements in finite fields

1 citations · 1 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2025

Existence of primitive k-normal elements for critical values over finite fields

Josimar J. R. Aguirre, Sarah F. M. Mazzini, Victor G. L. Neumann

Let $F_{q^{n}}$ be a finite field with $q^{n}$ elements. An element $α \in F_{q^{n}}$ is called $k$ -normal over $F_{q}$ if $α$ and its conjugates generate a vecto…

math.NT2024

On the functional graph of $f (X) = X (X^{q - 1} - c)^{q + 1},$ over quadratic extensions of finite fields

Josimar J. R. Aguirre, Abílio Lemos, Victor G. L. Neumann

Let $F_{q}$ be the finite field with $q$ elements. In this paper we will describe the dynamics of the map $f (X) = X (X^{q - 1} - c)^{q + 1},$ with $c \in F_{q}^{*},$ over…

math.NT2022

$r$ -primitive $k$ -normal elements in arithmetic progressions over finite fields

Josimar J. R. Aguirre, Abílio Lemos, Victor G. L. Neumann +1

Let $F_{q^{n}}$ be a finite field with $q^{n}$ elements. For a positive divisor $r$ of $q^{n} - 1$ , the element $α \in F_{q^{n}}^{*}$ is called \textit{ $r$ -primitive} if its m…

math.NT2022

Pairs of $r$ -primitive and $k$ -normal elements in finite fields

Josimar J. R. Aguirre, Victor G. L. Neumann

Let $F_{q^{n}}$ be a finite field with $q^{n}$ elements and $r$ be a positive divisor of $q^{n} - 1$ . An element $α \in F_{q^{n}}^{*}$ is called $r$ -primitive if its multiplic…

math.CO2022

Number of $k$ -normal elements over a finite field

Josimar J. R. Aguirre, Victor G. L. Neumann

An element $α \in F_{q^{n}}$ is a normal element over $F_{q}$ if the conjugates $α^{q^{i}}$ , $0 \leq i \leq n - 1$ , are linearly independent over $F_{q}$ . Hence a n…

math.NT2021

About $r$ - primitive and $k$ -normal elements in finite fields

Cícero Carvalho, Josimar J. R. Aguirre, Victor G. L. Neumann

In 2013, Huczynska, Mullen, Panario and Thomson introduced the concept of $k$ -normal elements: an element $α \in F_{q^{n}}$ is $k$ -normal over $F_{q}$ if the greatest…

Existence of primitive k-normal elements for critical values over finite fields

On the functional graph of f(X)=X(Xq−1−c)q+1, over quadratic extensions of finite fields

r-primitive k-normal elements in arithmetic progressions over finite fields

Pairs of r-primitive and k-normal elements in finite fields

Number of k-normal elements over a finite field

About r- primitive and k-normal elements in finite fields

On the functional graph of $f (X) = X (X^{q - 1} - c)^{q + 1},$ over quadratic extensions of finite fields

$r$ -primitive $k$ -normal elements in arithmetic progressions over finite fields

Pairs of $r$ -primitive and $k$ -normal elements in finite fields

Number of $k$ -normal elements over a finite field

About $r$ - primitive and $k$ -normal elements in finite fields