8 papers
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…
Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves
Monica Lichtenwalner, Hiram H. López, Gretchen L. Matthews +1
Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphis…
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…
A repair scheme for a distributed storage system based on multivariate polynomials
Hiram H. López, Gretchen L. Matthews, Daniel Valvo
A distributed storage system stores data across multiple nodes, with the primary objective of enabling efficient data recovery even in the event of node failures. The main goal 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…