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Optimal quantum locally recoverable codes from matrix-product construction

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arxiv 2310.15703 v2 pith:TKKTNPCP submitted 2023-10-24 cs.IT math.IT

Carlos Galindo , Fernando Hernando , Carlos Munuera , Diego Ruano This is my paper · ORCID
classification cs.ITmath.IT
keywords codesquantumlrcsmathcalclassicallocallyoptimalrecoverable
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large scale distributed and cloud storage systems. Quantum locally recoverable codes (quantum LRCs) are the quantum counterpart of classical LRCs. They allow us to correct erasures at several positions from a trace-preserving quantum operation acting on qudits of a larger set of positions. Parameters and localities of quantum LRCs satisfy a Singleton-like bound; codes attaching this bound are named to be optimal. Quantum LRCs, $\mathcal{Q}(\mathcal{C})$, can be constructed from classical Hermitian (or Euclidean) dual containing codes $\mathcal{C}$, and their recovery abilities are upper bounded by the minimum distance of the Hermitian (or Euclidean) dual of those codes. We consider matrix-product codes (MPCs) $\mathcal{C}$ and give constituent matrices and conditions on the constituent codes such that the codes $\mathcal{C}$ satisfy the conditions to provide quantum LRCs. As consequence, we are able to provide the locality and parameters of the quantum LRCs $\mathcal{Q}(\mathcal{C})$ and determine families of optimal quantum LRCs derived from them.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement-Assisted Quantum Locally Recoverable Codes: Characterizations, Bounds, and Constructions

    cs.IT 2026-07 accept novelty 7.0 of 10

    First explicit optimal pure CSS-like EAQLRC families are constructed from ℓ-intersection MDS pairs and block parity-check matrices, with Singleton-like optimality and nontrivial locality.

  2. Information locality of a quantum locally recoverable code

    quant-ph 2026-08 accept novelty 6.0 of 10

    For quantum codes built from finite-field linear codes, a more accurate locality measure and an algorithm reduce the number of qudits and measurements needed for erasure repair.

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