{
  "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$(r,\\delta)$(quantum$(r,\\delta)$-LRCs) are the quantum counterpart of classical$(r,\\delta)$-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$(r,\\delta)$-LRCs,$\\mathcal {Q}(\\mathcal {C})$, can be constructed from classical Euclidean (or Hermitian) dual-containing codes$\\mathcal {C}$, 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$(r,\\delta)$-LRCs satisfy a Singleton-like bound; codes attaining equality are referred to as optimal. We consider matrix-product codes (MPCs)$\\mathcal {C}$and give constituent (or defining) matrices and conditions on the constituent codes such that the codes$\\mathcal {C}$satisfy the conditions to provide quantum$(r,\\delta)$-LRCs. As a consequence, we are able to determine their locality and parameters. Furthermore, we determine families of optimal pure quantum$(r,\\delta)$-LRCs derived from them.",
  "abstract_shown": true,
  "affiliations": [
    "Institut Universitari de Matemàtiques i Aplicacions de Castelló, Universitat Jaume I, Campus de Riu Sec",
    "IMUVA-Mathematics Research Institute, Universidad de Valladolid"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Carlos Galindo",
      "orcid": "0000-0002-3908-4462"
    },
    {
      "affs": [
        0
      ],
      "name": "Fernando Hernando",
      "orcid": "0000-0002-9758-2152"
    },
    {
      "affs": [
        1
      ],
      "name": "Carlos Munuera",
      "orcid": "0000-0001-8386-3060"
    },
    {
      "affs": [
        1
      ],
      "name": "Diego Ruano",
      "orcid": "0000-0001-7304-0087"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vxhaqpp0dxdx.bib",
  "cited_by": 10,
  "doi": "10.1109/tit.2026.3728531",
  "fulltext_url": null,
  "id": "2vxhaqpp0dxdx",
  "issns": [
    "0018-9448",
    "1557-9654"
  ],
  "landing_url": "https://doi.org/10.1109/tit.2026.3728531",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7204540550",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": "Institute of Electrical and Electronics Engineers",
  "ris": "https://research.draconitic.com/paper/2vxhaqpp0dxdx.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W7204540550",
      "source": "openalex",
      "url": "https://doi.org/10.1109/tit.2026.3728531"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Coding theory and cryptography",
      "subfield": "combinatorics"
    }
  ],
  "title": "Optimal Pure Quantum ( r , δ )-Locally Recoverable Codes From Matrix-Product Construction",
  "title_text": "Optimal Pure Quantum ( r , δ )-Locally Recoverable Codes From Matrix-Product Construction",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/2vxhaqpp0dxdx",
  "venue": "IEEE Transactions on Information Theory",
  "versions": []
}