Luciane Quoos

activity

20112024

most citedOne- and Two-Point Codes over Kummer Extensions

19 citations · 39 across the 18 of their papers we have counts for

collaborators

23 papers

math.AG2024

Linear Complementary dual codes and Linear Complementary pairs of AG codes in function fields

Alonso S. Castellanos, Adler V. Marques, Luciane Quoos

In recent years, linear complementary pairs (LCP) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory an…

cs.IT2024

Self-orthogonal flags of codes and translation of flags of algebraic geometry codes

Maria Bras-Amorós, Alonso S. Castellanos, Luciane Quoos

A flag $C_{0} ⊊ C_{1} \dots ⊊ C_{s} ⊊ F_{q}^{n}$ of linear codes is said to be self-orthogonal if the duals of the codes in the flag satisfy $C_{i}^\pe…

math.NT2024

Some families of non-isomorphic maximal function fields

Peter Beelen, Maria Montanucci, Jonathan Tilling Niemann +1

The problem of understanding whether two given function fields are isomorphic is well-known to be difficult, particularly when the aim is to prove that an isomorphism does not exis…

cs.IT2023

Lifting iso-dual algebraic geometry codes

María Chara, Ricardo Podestá, Luciane Quoos +1

In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field $F_{q}$ with $q$ elements. Given a finite separable extension…

math.NT2023

Cyclotomic function fields over finite fields with irreducible quadratic modulus

Nazar Arakelian, Luciane Quoos

Let $F_{q}$ be the finite field of order $q$ and $F = F_{q} (x)$ the rational function field. In this paper, we give a characterization of the cyclotomic function fields…

math.AG2023★ 2 cited

Weierstrass Semigroup, Pure Gaps and Codes on Function Fields

Alonso S. Castellanos, Erik A. R. Mendoza, Luciane Quoos

We determine the Weierstrass semigroup at one and two totally ramified places in a Kummer extension defined by the affine equation $y^{m} = \prod_{i = 1}^{r} (x - α_{i})^{λ_{i}}$ over $K$ , t…

math.NT2021

Reciprocal polynomials and curves with many points over a finite field

Rohit Gupta, Erik A. R. Mendoza, Luciane Quoos

Let $F_{q^{2}}$ be the finite field with $q^{2}$ elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over…

cs.IT2021

Isometry-Dual Flags of Many-Point AG Codes

Maria Bras-Amorós, Alonso S. Castellanos, Luciane Quoos

Let $F_{q}$ be a finite field. A flag of $F_{q}$ -linear codes $C_{0} ⊊ C_{1} ⊊ \dots ⊊ C_{s}$ is said to satisfy the isometry-dual property if there exists a vector $x…

cs.IT2020

The Isometry-Dual Property in Flags of Two-Point Algebraic Geometry Codes

Maria Bras-Amorós, Alonso S. Castellanos, Luciane Quoos

A flag of codes $C_{0} ⊊ C_{1} ⊊ \dots ⊊ C_{s} \subseteq F_{q}^{n}$ is said to satisfy the {\it isometry-dual property} if there exists ${\bf x}\in (\ma…

math.AG2020

Locally recoverable codes from automorphism groups of function fields of genus $g \geq 1$

Daniele Bartoli, Maria Montanucci, Luciane Quoos

A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we hav…

cs.IT2019★ 6 cited

Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field

Alonso S. Castellanos, Luciane Quoos, Guilherme Tizziotti

For $r \geq 1$ an odd integer, we provide a sequence from the function field $F_{q, r}$ of the maximal curve over $F_{q^{2 r}}$ defined by the affine equation $y^…

math.AG2018

Explicit Maximal and Minimal Curves of Artin-Schreier Type from Quadratic Forms

Daniele Bartoli, Luciane Quoos, Zülfükar Saygı +1

In this work we present explicit examples of maximal and minimal curves over finite fields in odd characteristic. The curves are of Artin-Schreier type and the construction is clos…

math.CO2018★ 8 cited

Pure gaps on curves with many rational places

Daniele Bartoli, Ariane M. Masuda, Maria Montanucci +1

We consider the algebraic curve defined by $y^{m} = f (x)$ where $m \geq 2$ and $f (x)$ is a rational function over $F_{q}$ . We extend the concept of pure gap to {\bf c}-gap and…

math.CO2018

Permutation polynomials over $F_{q^{2}}$ from rational functions

Daniele Bartoli, Ariane M. Masuda, Luciane Quoos

Let $μ_{q + 1}$ denote the set of $(q + 1)$ -th roots of unity in $F_{q^{2}}$ . We construct permutation polynomials over $F_{q^{2}}$ by using rational functions of any de…

math.AG2017★ 1 cited

On the difference between permutation polynomials over finite fields

Nurdagül Anbar, Almasa Oduzak, Vandita Patel +3

The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that if $p > (d^{2} - 3 d + 4)^{2}$ , then there is no complete mapping polynomial $f$ in $\Fp[x]$ of degree $d…

math.AG2016

On some Galois covers of the Suzuki and Ree curves

Massimo Giulietti, Maria Montanucci, Luciane Quoos +1

We determine the full automorphism group of two recently constructed families $S ~_{q}$ and $R ~_{q}$ of maximal curves over finite fields. These curves…

math.AG2016★ 3 cited

Algebraic Geometric codes from Kummer Extensions

Daniele Bartoli, Luciane Quoos, Giovanni Zini

For Kummer extensions defined by $y^{m} = f (x)$ , where $f (x)$ is a separable polynomial over the finite field $F_{q}$ , we compute the number of Weierstrass gaps at two total…

math.CO2016

Complete permutation polynomials from exceptional polynomials

Daniele Bartoli, Massimo Giulietti, Luciane Quoos +1

We classify complete permutation polynomials of type $a X^{\frac{q ^{n} - 1}{q - 1} + 1}$ over the finite field with $q^{n}$ elements, for $n + 1$ a prime and $n^{4} < q$ . For the case $n + 1$ a pow…

math.AG2015★ 19 cited

One- and Two-Point Codes over Kummer Extensions

Ariane M. Masuda, Luciane Quoos, Alonso Sepúlveda

We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by $y^{m} = f (x)^{λ}$ where $f (x)$ is a separable polynomial over $F_{q}$ . In addi…

math.AG2015

Maximal curves from subcovers of the GK-curve

Massimo Giulietti, Luciane Quoos, Giovanni Zini

For every $q = n^{3}$ with $n$ a prime power greater than $2$ , the GK-curve is an $F_{q^{2}}$ -maximal curve that is not $F_{q^{2}}$ -covered by the Hermitian curve. In this…

math.RT2014

Character Theory of Monoids over an Arbitrary Field

Ariane M. Masuda, Luciane Quoos, Benjamin Steinberg

The basic character theory of finite monoids over the complex numbers was developed in the sixties and seventies based on work of Munn, Ponizovsky, McAlister, Rhodes and Zalcstein.…

math.AG2013

Weierstrass points on Kummer extensions

Miriam Abdon, Herivelto Borges, Luciane Quoos

For Kummer extensions $y^{m} = f (x)$ , we discuss conditions for an integer be a Weierstrass gap at a place $P$ . In the case of totally ramified places, the conditions will be necessary…

math.NT2011

Bases for Riemann-Roch spaces of one point divisors on an optimal tower of function fields

Francesco Noseda, Gilvan Oliveira, Luciane Quoos

For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We give an algor…

Linear Complementary dual codes and Linear Complementary pairs of AG codes in function fields

Self-orthogonal flags of codes and translation of flags of algebraic geometry codes

Some families of non-isomorphic maximal function fields

Lifting iso-dual algebraic geometry codes

Cyclotomic function fields over finite fields with irreducible quadratic modulus

Weierstrass Semigroup, Pure Gaps and Codes on Function Fields

Reciprocal polynomials and curves with many points over a finite field

Isometry-Dual Flags of Many-Point AG Codes

The Isometry-Dual Property in Flags of Two-Point Algebraic Geometry Codes

Locally recoverable codes from automorphism groups of function fields of genus g≥1

Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field

Explicit Maximal and Minimal Curves of Artin-Schreier Type from Quadratic Forms

Pure gaps on curves with many rational places

Permutation polynomials over Fq2​ from rational functions

On the difference between permutation polynomials over finite fields

On some Galois covers of the Suzuki and Ree curves

Algebraic Geometric codes from Kummer Extensions

Complete permutation polynomials from exceptional polynomials

One- and Two-Point Codes over Kummer Extensions

Maximal curves from subcovers of the GK-curve

Character Theory of Monoids over an Arbitrary Field

Weierstrass points on Kummer extensions

Bases for Riemann-Roch spaces of one point divisors on an optimal tower of function fields

Locally recoverable codes from automorphism groups of function fields of genus $g \geq 1$

Permutation polynomials over $F_{q^{2}}$ from rational functions