Lucas Reis

activity

20162026

most citedConstruction of irreducible polynomials through rational transformations

2 citations · 3 across the 14 of their papers we have counts for

collaborators

Showing 2017Show all

6 papers · 1 filter

math.NT2017

Variations of the Primitive Normal Basis Theorem

Giorgos Kapetanakis, Lucas Reis

The celebrated Primitive Normal Basis Theorem states that for any $n \geq 2$ and any finite field $F_{q}$ , there exists an element $α \in F_{q^{n}}$ that is simultaneously…

math.NT2017

On $k$ -normal elements over finite fields

Lucas Reis

The so called $k$ -normal elements appear in the literature as a generalization of normal elements over finite fields. Recently, questions concerning the construction of $k$ -normal…

math.NT2017

Existence of primitive $1$ -normal elements in finite fields

Lucas Reis, David Thomson

An element $α \in F_{q^{n}}$ is \emph{normal} if $B = {α, α^{q}, \dots, α^{q^{n - 1}}}$ forms a basis of $F_{q^{n}}$ as a vector space over $F_{q}$ ; in…

math.RA2017

A group action on multivariate polynomials over finite fields

Lucas Reis

Let $F_{q}$ be the finite field with $q$ elements, where $q$ is a power of a prime $p$ . Recently, a particular action of the group $GL_{2} (F_{q})$ on irreducibl…

math.NT2017

Invariant theory of a special group action on irreducible polynomials over finite fields

Lucas Reis

In the past few years, an action of $PGL_{2} (F_{q})$ on the set of irreducible polynomials in $F_{q} [x]$ has been introduced and many questions have been discuss…

math.NT2017

A note on primitive $1 -$ normal elements over finite fields

Lucas Reis

Let $q$ be a prime power of a prime $p$ , $n$ a positive integer and $F_{q^{n}}$ the finite field with $q^{n}$ elements. The $k -$ normal elements over finite fields were introduc…

Variations of the Primitive Normal Basis Theorem

On k-normal elements over finite fields

Existence of primitive 1-normal elements in finite fields

A group action on multivariate polynomials over finite fields

Invariant theory of a special group action on irreducible polynomials over finite fields

A note on primitive 1−normal elements over finite fields

On $k$ -normal elements over finite fields

Existence of primitive $1$ -normal elements in finite fields

A note on primitive $1 -$ normal elements over finite fields