Lucas Reis

activity

20152026

most citedCounting solutions of special linear equations over finite fields

6 citations · 16 across the 25 of their papers we have counts for

collaborators

Showing 2016Show all

4 papers · 1 filter

math.NT2016

Existence results on k-normal elements over finite fields

Lucas Reis

An element $α \in F_{q^{n}}$ is normal over $F_{q}$ if $α$ and its conjugates $α, α^{q}, \dots α^{q^{n - 1}}$ form a basis of $F_{q^{n}}$ over $F_{q}$ .…

math.NT2016

On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

Fabio E. Brochero Martínez, Theodoulos Garefalakis, Lucas Reis +1

In this paper, we find a lower bound for the order of the group $⟨ θ + α ⟩ \subset F_{q}^{*}$ , where $α \in F_{q}$ , $θ$ is a generic root of the po…

math.NT2016

Nilpotent linearized polynomials over finite fields and applications

Lucas Reis

Let $q$ be a prime power and $F_{q^{n}}$ be the finite field with $q^{n}$ elements, where $n > 1$ . We introduce the class of the linearized polynomials $L (x)$ over $\mathbb F_{q^…

math.NT2016

The action of $GL_{2} (F_{q})$ on irreducible polynomials over $\F_q$

Lucas Reis

Let $\F_q$ be the finite field with $q$ elements, $p=\Char \F_q$. The group $\GL_2(\F_q)$ acts naturally in the set of irreducible polynomials over $\F_q$ of degree at least $2$ . I…

Existence results on k-normal elements over finite fields

On the multiplicative order of the roots of bXqr+1−aXqr+dX−c

Nilpotent linearized polynomials over finite fields and applications

The action of GL2​(Fq​) on irreducible polynomials over $\F_q$

On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

The action of $GL_{2} (F_{q})$ on irreducible polynomials over $\F_q$