19 citations · 27 across the 13 of their papers we have counts for
15 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 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…
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…
Self-orthogonal flags of codes and translation of flags of algebraic geometry codes
Maria Bras-Amorós, Alonso S. Castellanos, Luciane Quoos
A flag of linear codes is said to be self-orthogonal if the duals of the codes in the flag satisfy $C_{i}^\pe…
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…
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 over , t…
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…
Isometry-Dual Flags of Many-Point AG Codes
Maria Bras-Amorós, Alonso S. Castellanos, Luciane Quoos
Let be a finite field. A flag of -linear codes is said to satisfy the isometry-dual property if there exists a vector $x…
The Isometry-Dual Property in Flags of Two-Point Algebraic Geometry Codes
Maria Bras-Amorós, Alonso S. Castellanos, Luciane Quoos
A flag of codes is said to satisfy the {\it isometry-dual property} if there exists ${\bf x}\in (\ma…
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^…
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}…
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 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 …
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 where is a separable polynomial over . In addi…