19 citations · 45 across the 14 of their papers we have counts for
14 papers
On decoding hyperbolic codes
Eduardo Camps-Moreno, Ignacio García-Marco, Hiram H. López +3
This work studies several decoding algorithms for hyperbolic codes. We use some previous ideas to describe how to decode a hyperbolic code using the largest Reed-Muller code contai…
On the affine permutation group of certain decreasing Cartesian codes
Eduardo Camps-Moreno, Hiram H. López, Eliseo Sarmiento +1
A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (s…
The minimum distance of a parameterized code over an even cycle
Eduardo Camps-Moreno, Jorge Neves, Eliseo Sarmiento
We compute the minimum distance of the parameterized code of order 1 over an even cycle.
On the generalized Hamming weights of hyperbolic codes
Eduardo Camps-Moreno, Ignacio García-Marco, Hiram H. López +3
A hyperbolic code is an evaluation code that improves a Reed-Muller because the dimension increases while the minimum distance is not penalized. We give the necessary and sufficien…
On the Waldschmidt constant of square-free principal Borel ideals
Eduardo Camps Moreno, Craig Kohne, Eliseo Sarmiento +1
Fix a square-free monomial . The square-free principal Borel ideal generated by , denoted , is the ideal generated by all…
Powers of Principal -Borel ideals
Eduardo Camps Moreno, Craig Kohne, Eliseo Sarmiento +1
Fix a poset on . A -Borel monomial ideal is a monomial ideal whose monomials are closed under the Borel-like mov…
Polar decreasing monomial-Cartesian codes
Eduardo Camps, Hiram H. López, Gretchen L. Matthews +1
We prove that families of polar codes with multiple kernels over certain symmetric channels can be viewed as polar decreasing monomial-Cartesian codes, offering a unified treatment…
Relative Generalized Minimum Distance Functions
Manuel Gonzalez Sarabia, Miguel E. Uribe-paczka, Eliseo Sarmiento +1
In this paper we introduce the relative generalized minimum distance function (RGMDF for short) and it allows us to give an algebraic approach to the relative generalized Hamming w…
Vanishing Ideals Of Affine Sets Parameterized By Odd Cycles
Miguel Eduardo Uribe Paczka, Eliseo Sarmiento, Carlos Rentería Márquez
Let K be a finite field. Let X* be a subset of the affine space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gröbner basis for the vanishing ideal, I…
The second generalized Hamming weight of some evaluation codes arising from a projective torus
Manuel González Sarabia, Eduardo Camps, Eliseo Sarmiento +1
In this paper we find the second generalized Hamming weight of some evaluation codes arising from a projective torus, and it allows to compute the second generalized Hamming weight…
On the Connectedness and Diameter of a Geometric Johnson Graph
Crevel Bautista-Santiago, Javier Cano, Ruy Fabila-Monroy +5
Let be a set of points in general position in the plane. A subset of is called an \emph{island} if there exists a convex set such that . In this p…
Parameterized affine codes
Hiram H. Lopez, Eliseo Sarmiento, Maria Vaz Pinto +1
Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Groebner bases, to compute the length and the dim…
On the vanishing ideal of an algebraic toric set and its parameterized linear codes
Eliseo Sarmiento, Maria Vaz Pinto, Rafael H. Villarreal
Let K be a finite field and let X be a subset of a projective space, over the field K, which is parameterized by monomials arising from the edges of a clutter. We show some estimat…
The minimum distance of parameterized codes on projective tori
Eliseo Sarmiento, Maria Vaz Pinto, Rafael H. Villarreal
Let X be a subset of a projective space, over a finite field K, which is parameterized by the monomials arising from the edges of a clutter. Let I(X) be the vanishing ideal of X. I…