6 citations · 10 across the 19 of their papers we have counts for
22 papers
Permutation Decoding of AG Codes from Curves Defined by Separated Polynomials
Alonso S. Castellanos, Guilherme Tizziotti, Wilson Olaya-León
In this work, we investigate permutation decoding for algebraic geometry (AG) codes arising from algebraic curves defined by separated polynomials. Using automorphisms of the under…
On planar functions over
João Paulo Guardieiro, Adler Marques, Luciane Quoos +1
Let denote the finite field of order . For odd, we investigate the planarity over of the family $$ f_{E,A,B,C,D}(X) := EX^2+ AX^{q+1}+ BX^{…
A closed formula for the Geil-Matsumoto bound on numerical semigroups via Apéry sets
Adler Marques, Erik Mendoza, Luciane Quoos +1
The Geil-Matsumoto bound (GM bound) constrains the number of rational points on a curve over a finite field in terms of the Weierstrass semigroup of any of the points on the curve.…
On generalized Weierstrass Semigroups in arbitrary Kummer extensions of
Alonso S. Castellanos, Erik A. R. Mendoza, Guilherme Tizziotti
In this work, we investigate generalized Weierstrass semigroups in arbitrary Kummer extensions of function field . We analyze their structure and properties, with…
The Set of Pure Gaps at Several Rational Places in Function Fields
Alonso S. Castellanos, Erik A. R. Mendoza, Guilherme Tizziotti
In this work, using maximal elements in generalized Weierstrass semigroups and its relationship with pure gaps, we extend the results in \cite{CMT2024} and provide a way to complet…
On atoms of the set of generalized numerical semigroups with fixed corner element
Matheus Bernardini, Alonso S. Castellanos, Wanderson Tenório +1
We study the so-called atomic GNS, which naturally extends the concept of atomic numerical semigroup. We introduce the notion of corner special gap and we characterize the class of…
Complete set of Pure Gaps in Function Fields
Alonso S. Castellanos, Erik A. R. Mendoza, Guilherme Tizziotti
In this work, we provide a way to completely determine the set of pure gaps at two rational places in a function field over a finite field $\mathbb{F…
On the automorphism group of a family of maximal curves not covered by the Hermitian curve
Maria Montanucci, Guilherme Tizziotti, Giovanni Zini
In this paper we compute the automorphism group of the curves and introduced in Tafazolian et al. in 2016 as new examples of maximal cur…
The corner element of generalized numerical semigroups
Matheus Bernardini, Wanderson Tenório, Guilherme Tizziotti
In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalize…
Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve
M. Montanucci, G. Tizziotti
In this paper we determine the generalized Weierstrass semigroup , and consequently the Weierstrass semigroup $H(P_{\infty}, P_1, \ld…
On the existence of pairs of primitive and normal elements over finite fields
Cícero Carvalho, João Paulo Guardieiro, Victor G. L. Neumann +1
Let be a finite field with elements, and let and be positive integers. Given polynomials with $\textrm{deg…
On existence of some special pair of primitive elements over finite fields
C. Carvalho, J. P. G. Sousa, V. G. L. Neumann +1
In this paper we generalize the results of Sharma, Awasthi and Gupta (see \cite{SAG}). We work over a field of any characteristic with elements and we give a sufficient c…
Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field
Alonso S. Castellanos, Luciane Quoos, Guilherme Tizziotti
For an odd integer, we provide a sequence from the function field of the maximal curve over defined by the affine equation $y^…
On Weierstrass gaps at several points
Wanderson Tenório, Guilherme Tizziotti
We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups d…
Subcovers and codes on the curves
Herivelto Borges, Alonso S. Castellanos, Guilherme Tizziotti
In this work, subcovers of the curve are constructed, the Weierstrass semigroup at the point $P_\infty \in \mathcal{X}_{n,r}…
Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables
Wanderson Tenório, Guilherme Tizziotti
In this work we study the generalized Weierstrass semigroup at an -tuple of rational points on certain curv…
Weierstrass Semigroup and Pure Gaps at several points on the curve
Alonso S. Castellanos, Guilherme Tizziotti
We determine the Weierstrass semigroup at several points on the curve. In addition, we present conditions to find pure gaps on the set o…
On Gröbner Basis for certain one-point AG codes
Federico Fornasiero, Guilherme Tizziotti
In this work we present a way to construct the so-called root diagram for one-point AG codes arising from certain types of curves over with plane m…
On Weierstrass semigroup at points on curves of the type f(y) = g(x)
A. S. Castellanos, G. Tizziotti
In this work we determine the so-called minimal generating set of the Weierstrass semigroup of certain points on curves with plane model of the type …
On k-sparse numerical semigroups
G. Tizziotti, J. Villanueva
Given a positive integer k, we investigate the class of numerical semigroups verifying the property that every two subsequent non gaps, smaller than the conductor, are spaced by at…
Two-point AG codes on the GK maximal curves
Alonso Sepúlveda, Guilherme Tizziotti
We determine de Weierstrass semigroup of a pair of certain rational points on the GK-curves. We use this semigroup to obtain two-point AG codes with better parameters than comparab…
Weierstrass semigroup and Automorphism group of the curves
Herivelto Borges, Alonso Sepúlveda, Guilherme Tizziotti
In this paper, we determine the Weierstrass semigroup and the full automorphism group of a certain family of curves , which was recently introduc…