7 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…
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}…