{
  "abstract": "Ferrers diagram rank-metric codes are essential components of the multilevel construction of constant dimension codes for random network coding. This paper aims to construct optimal Ferrers diagram rank-metric codes, focusing on the diagram \\([3,3,3,5]\\) with rank distance \\(3\\). We construct an optimal \\([[3,3,3,5],6,3]_q\\) Ferrers diagram rank-metric code for every prime power \\(q\\), thereby answering an open problem posed by Etzion et al. in 2016~\\cite{Etzion2016}. The construction first builds a \\([3\\times4,4,3]_q\\) MRD code and then proves that the Delsarte dual of its puncturing on the last column contains a \\([3\\times3,3,3]_q\\) MRD code, which comes from semifield codes. We further construct optimal Ferrers diagram rank-metric codes for two infinite families of Ferrers diagrams: the first relies on the \\([[3,3,3,5],6,3]_q\\) construction and holds for every prime power \\(q\\), while the second is binary and obtained directly by the puncturing-inclusion construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17570",
  "author_total": 4,
  "authors": [
    {
      "name": "Dengming Xu"
    },
    {
      "name": "Chengming Duan"
    },
    {
      "name": "Yong Jin"
    },
    {
      "name": "Yuhao Ning"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bqg68jk4cewp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17570",
  "fulltext_url": null,
  "id": "6bqg68jk4cewp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17570",
  "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": "W7221760801",
  "pdf_url": "https://arxiv.org/pdf/2610.17570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bqg68jk4cewp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17570"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Puncturing-inclusion constructions of optimal Ferrers diagram rank-metric codes using semifield codes",
  "title_text": "Puncturing-inclusion constructions of optimal Ferrers diagram rank-metric codes using semifield codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/6bqg68jk4cewp",
  "venue": "arXiv",
  "versions": []
}