Optimal Pure Quantum ( r , δ )-Locally Recoverable Codes From Matrix-Product Construction
- 1Institut Universitari de Matemàtiques i Aplicacions de Castelló, Universitat Jaume I, Campus de Riu Sec
- 2IMUVA-Mathematics Research Institute, Universidad de Valladolid
Abstract
Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large-scale distributed and cloud storage systems. Quantum locally recoverable codes of locality(r,δ)(quantum(r,δ)-LRCs) are the quantum counterpart of classical(r,δ)-LRCs. They allow us to correct erasures at several positions using a trace-preserving quantum operation acting on qudits of a larger set of positions. Quantum(r,δ)-LRCs,𝒬(𝒞), can be constructed from classical Euclidean (or Hermitian) dual-containing codes𝒞, and their recovery abilities are upper bounded by the minimum distance of the Euclidean (or Hermitian) dual of those codes. Parameters and localities of pure quantum(r,δ)-LRCs satisfy a Singleton-like bound; codes attaining equality are referred to as optimal. We consider matrix-product codes (MPCs)𝒞and give constituent (or defining) matrices and conditions on the constituent codes such that the codes𝒞satisfy the conditions to provide quantum(r,δ)-LRCs. As a consequence, we are able to determine their locality and parameters. Furthermore, we determine families of optimal pure quantum(r,δ)-LRCs derived from them.
Related
- Optimal Quantum ( r , δ )-Locally Repairable Codes From Matrix-Product Codes
- Beyond Polynomials: Optimal Locally Recoverable Codes from Good Rational Functions
- Alphabet-Dependent Bounds for Pure Quantum (r,ρ)-Locally Recoverable Codes
- Asymmetric Entanglement-Assisted Quantum Locally Recoverable Codes
- Good Quantum Locally Testable Codes from Product Expansion
BibTeX
@article{galindo2026optimal,
title = {{Optimal Pure Quantum ( r , δ )-Locally Recoverable Codes From Matrix-Product Construction}},
author = {Carlos Galindo and Fernando Hernando and Carlos Munuera and Diego Ruano},
journal = {IEEE Transactions on Information Theory},
year = {2026},
month = aug,
doi = {10.1109/tit.2026.3728531},
url = {https://doi.org/10.1109/tit.2026.3728531},
note = {CC BY},
}
RIS
TY - JOUR
TI - Optimal Pure Quantum ( r , δ )-Locally Recoverable Codes From Matrix-Product Construction
AU - Carlos Galindo
AU - Fernando Hernando
AU - Carlos Munuera
AU - Diego Ruano
PY - 2026
DA - 2026/08/28
JO - IEEE Transactions on Information Theory
DO - 10.1109/tit.2026.3728531
UR - https://doi.org/10.1109/tit.2026.3728531
AB - Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large-scale distributed and cloud storage systems. Quantum locally recoverable codes of locality(r,δ)(quantum(r,δ)-LRCs) are the quantum counterpart of classical(r,δ)-LRCs. They allow us to correct erasures at several positions using a trace-preserving quantum operation acting on qudits of a larger set of positions. Quantum(r,δ)-LRCs,𝒬(𝒞), can be constructed from classical Euclidean (or Hermitian) dual-containing codes𝒞, and their recovery abilities are upper bounded by the minimum distance of the Euclidean (or Hermitian) dual of those codes. Parameters and localities of pure quantum(r,δ)-LRCs satisfy a Singleton-like bound; codes attaining equality are referred to as optimal. We consider matrix-product codes (MPCs)𝒞and give constituent (or defining) matrices and conditions on the constituent codes such that the codes𝒞satisfy the conditions to provide quantum(r,δ)-LRCs. As a consequence, we are able to determine their locality and parameters. Furthermore, we determine families of optimal pure quantum(r,δ)-LRCs derived from them.
SN - 0018-9448
SN - 1557-9654
ER -