{
  "abstract": "The dimension of a Galois hull is an important parameter in the construction of entanglement-assisted quantum error-correcting codes. In this paper, we study generalized Roth-Lempel (GRL) codes with prescribed Galois hull dimensions over finite fields of arbitrary characteristic. We develop a common construction method based on normalized Lagrange coefficients and suitable choices of column multipliers, and obtain six explicit constructions from multiplicative cosets, trace fibers, additive-subspace cosets, and mixed additive--multiplicative fibers. For extension sizes $s=2$ and $s=3$, we construct MDS and AMDS GRL codes with Galois hulls of specific dimensions. The resulting codes provide EAQECCs with explicit dimension, entanglement consumption, and relatively large minimum distance. Taking zero-dimensional hulls also gives Hermitian LCD GRL codes and the corresponding maximally entangled EAQECCs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20453",
  "author_total": 4,
  "authors": [
    {
      "name": "Xuefei Wu"
    },
    {
      "name": "Qi Liu"
    },
    {
      "name": "Yingchun Chen"
    },
    {
      "name": "Haiyan Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fryyk15br4fz1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20453",
  "fulltext_url": null,
  "id": "fryyk15br4fz1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20453",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7213584710",
  "pdf_url": "https://arxiv.org/pdf/2609.20453",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fryyk15br4fz1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20453",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20453"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs",
  "title_text": "Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/fryyk15br4fz1",
  "venue": "arXiv",
  "versions": []
}