4 papers
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…
Bounds and MacWilliams Identities for codes over Artinian rings
Eduardo Camps-Moreno, Carlos Espinosa-Valdéz, Hiram H. López +2
This work develops new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal nu…