2 citations · 2 across the 10 of their papers we have counts for
10 papers
On generalized Weierstrass semigroups in linearized function fields
Erik Mendoza
In this article, using the notion of discrepancies, we study the generalized Weierstrass semigroup , where is an -tuple of distinct totally…
Characterization of non-special divisors of small degree on Kummer extensions and LCP codes
Erik Mendoza, Horacio Navarro, Luciane Quoos
A recent construction of linear complementary pairs (LCPs) of algebraic geometry codes is intimately linked to the identification of non-special divisors of small degree within a f…
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 gap sets in arbitrary Kummer extensions of
Ethan Cotterill, Erik A. R. Mendoza, Pietro Speziali
Let be an algebraically closed field, and let be a Kummer extension of function fields of genus . We provide a compact and explicit description of the gap set $G(Q)…
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…
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…
On Kummer extensions with one place at infinity
Erik A. R. Mendoza
Let be the algebraic closure of . We provide an explicit description of the Weierstrass semigroup at the only place at infinity of th…
Reciprocal polynomials and curves with many points over a finite field
Rohit Gupta, Erik A. R. Mendoza, Luciane Quoos
Let be the finite field with elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over…