5 papers
Duals of multiplicity codes
Eduardo Camps Moreno, Adrián Fidalgo-DÃaz, Hiram H. López +3
Multivariate multiplicity codes have been recently explored because of their importance for list decoding and local decoding. Given a multivariate multiplicity code, in this paper,…
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…
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…
Hulls of projective Reed-Muller codes over the projective plane
Diego Ruano, Rodrigo San-José
By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull and the Hermitian hull of projective Reed-Muller codes over the projective plane. The dim…
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,…