Vincenzo Pallozzi Lavorante

activity

20192025

collaborators

9 papers

math.AG2025

Evaluation codes arising from symmetric polynomials

Barbara Gatti, Gábor Korchmáros, Gábor P. Nagy +2

Datta and Johnsen (Des. Codes and Cryptogr., {\bf{91}} (2023), 747-761) introduced a new family of evalutation codes in an affine space of dimension $\geq 2$ over a finite field $\m…

cs.IT2024

Codes from $A_{m}$ -invariant polynomials

Giacomo Micheli, Vincenzo Pallozzi Lavorante, Phillip Waitkevich

Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $F_{q} [x_{1}, \dots, x_{m}]$ combined with the ide…

math.RA2023

An approach to normal polynomials through symmetrization and symmetric reduction

Darien Connolly, Calvin George, Xiang-dong Hou +2

An irreducible polynomial $f \in F_{q} [X]$ of degree $n$ is {\em normal} over $F_{q}$ if and only if its roots $r, r^{q}, \dots, r^{q^{n - 1}}$ satisfy the condition $Δ_n(r, r^q,\dot…

math.NT2022

A General Construction of Permutation Polynomials of $F_{q^{2}}$

Xiang-dong Hou, Vincenzo Pallozzi Lavorante

Let $r$ be a positive integer, $h (X) \in F_{q^{2}} [X]$ , and $μ_{q + 1}$ be the subgroup of order $q + 1$ of $F_{q^{2}}^{*}$ . It is well known that $X^{r} h (X^{q - 1})$ permutes $\Bbb F_{q…

math.NT2021

On permutation quadrinomials from Niho exponents in characteristic two

Vincenzo Pallozzi Lavorante

In a recent paper Zheng et al. characterized the coefficients of $f (x) = x + a_{1} x^{s_{1} (2 m - 1) + 1} + a_{2} x^{s_{2} (2 m - 1) + 1} + a_{3} x^{s_{3} (2 m - 1) + 1}$ over $F_{2}^{2 m}$ that lead $ f…

math.NT2021

New Results on Permutation Binomials of Finite Fields

Xiang-dong Hou, Vincenzo Pallozzi Lavorante

After a brief review of existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bri…

math.CO2021

New families of permutation trinomials constructed by permutations of $μ_{q + 1}$

Vincenzo Pallozzi Lavorante

Permutation polynomials are of particular significance in several areas of applied mathematics, such as Coding theory and Cryptography. Many recent constructions are based on the A…

math.CO2021

External points to a conic from a Baer subplane

Vincenzo Pallozzi Lavorante

For an irreducible conic $C$ in a Desarguesian plane of odd square order, estimating the number of points from a Baer subplane which are external to $C$ is a natu…

math.AG2019

AG codes from the second generalization of the GK maximal curve

Maria Montanucci, Vicenzo Pallozzi Lavorante

The second generalized GK maximal curves $G K_{2, n}$ are maximal curves over finite fields with $q^{2 n}$ elements, where $q$ is a prime power and $n \geq 3$ an odd integer…

Evaluation codes arising from symmetric polynomials

Codes from Am​-invariant polynomials

An approach to normal polynomials through symmetrization and symmetric reduction

A General Construction of Permutation Polynomials of Fq2​

On permutation quadrinomials from Niho exponents in characteristic two

New Results on Permutation Binomials of Finite Fields

New families of permutation trinomials constructed by permutations of μq+1​

External points to a conic from a Baer subplane

AG codes from the second generalization of the GK maximal curve

Codes from $A_{m}$ -invariant polynomials

A General Construction of Permutation Polynomials of $F_{q^{2}}$

New families of permutation trinomials constructed by permutations of $μ_{q + 1}$