8 papers
Maximum number of zeroes of polynomials on weighted projective spaces over a finite field
Jade Nardi, Rodrigo San-José
We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is…
Reed-Muller type codes over a combinatorial simplex: an algebraic description
Hiram H. López, Rodrigo San-José, Nart Shalqini
Given an ordered set of a finite field, a combinatorial simplex over is defined as the set of vectors such that the positions of the entries, with respect to , sum up to…
Private neighbors, perfect codes and their relation with the -number of closed neighborhood ideals
Delio Jaramillo-Velez, Hiram H. López, Rodrigo San-José
In this work, we investigate the connections between dominating sets, private neighbors, and perfect codes in graphs, and their relationships with commutative algebra. In particula…
Structure of weighted projective Reed-Muller codes
Jade Nardi, Rodrigo San-José
We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some…
Transversal gates for quantum CSS codes
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +2
In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of…
Cartesian square-free codes
CÃcero Carvalho, Hiram H. López, Rodrigo San-José
The generalized Hamming weights (GHWs) of a linear code C extend the concept of minimum distance, which is the minimum cardinality of the support of all one-dimensional subspaces o…