6 papers · 1 filter
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…
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
Cícero 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…
Code distances: a new family of invariants of linear codes
Eduardo Camps-Moreno, Elisa Gorla, Hiram H. López
In this paper, we introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are…