Quantum error-correcting codes from projective Reed–Muller codes and their hull variation problem
Year: 2025
Type: article
Abstract: Long quantum codes using projective Reed–Muller codes are constructed. Projective Reed–Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum codes by using the CSS construction and the Hermitian construction, respectively. We provide entanglement-assisted quantum error-correcting codes from projective Reed–Muller codes with flexible amounts of entanglement by considering equivalent codes. Moreover, we also construct quantum codes from subfield subcodes of projective Reed–Muller codes.
Authors: Diego Ruano, Rodrigo San-José
Institution: Universidad de Valladolid
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407425576