9 citations · 17 across the 13 of their papers we have counts for
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The permutation and automorphism groups of univariate multiplicity codes
Eduardo Camps Moreno, Hiram H. López, Umberto Martínez-Peñas +1
We give explicit characterizations of the permutations and linear isometries that leave (univariate) multiplicity codes invariant. We consider any evaluation subset of the finite f…
Asymptotically good binary triorthogonal codes and higher-level transversal gates
Rodrigo San-José
For each level of the Clifford hierarchy from the third level onward, we construct explicit asymptotically good binary CSS codes for which a strongly transversal diagonal rotation,…
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…
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
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…
Hermitian hull of some GRS codes and new EAQMDS codes
Oisin Campion, Rodrigo San-José
We study the Hermitian hull of a particular family of generalized Reed-Solomon codes. The problem of computing the dimension of the hull is translated to a counting problem in a la…
Binary Triorthogonal and CSS-T Codes for Quantum Error Correction
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +3
In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respec…
An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance
Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews +3
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1,…
Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem
Diego Ruano, Rodrigo San-José
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the proje…
Subfield subcodes of projective Reed-Muller codes
Philippe Gimenez, Diego Ruano, Rodrigo San-José
Explicit bases for the subfield subcodes of projective Reed-Muller codes over the projective plane and their duals are obtained. In particular, we provide a formula for the dimensi…