{
  "abstract": "Maximum-likelihood decoding of linear codes over erasure channels can be considered as solving a linear system of a column submatrix of the parity-check matrix. In practice, Gaussian elimination is usually applied, and its computational cost depends on the structure of the matrix, especially the sparsity and the fill-in generated during the elimination. The \\emph{chordal graph}, or \\emph{triangulated graph}, first introduced by C. Berge, has a so-called \\emph{perfect elimination ordering}, indicating that if the primal graph of a matrix is a chordal graph, then there exists a perfect elimination ordering such that a special class of fill-in under Gaussian elimination following this ordering will be avoided. In this paper, we introduce \\emph{chordal codes}, i.e., codes equipped with parity-check matrices such that the primal graphs of the parity-check matrices are chordal. We prove that, for a chordal code, the decoding submatrix associated with any erasure pattern retains a chordal primal graph. So, the complexity of chordal elimination (Gaussian elimination following the perfect elimination ordering applied to the chordal code decoding) will be smaller than decoding a random code by Gaussian elimination. Also, we provide an upper bound on the complexity of chordal elimination.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17934",
  "author_total": 4,
  "authors": [
    {
      "name": "Yulin Chen"
    },
    {
      "name": "Laigang Guo"
    },
    {
      "name": "Tong Li"
    },
    {
      "name": "Mingyang Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7arz4kjkk501z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17934",
  "fulltext_url": null,
  "id": "7arz4kjkk501z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17934",
  "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": "W7221750539",
  "pdf_url": "https://arxiv.org/pdf/2610.17934",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7arz4kjkk501z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17934",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17934"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Chordal Codes: Code Construction and Efficient Gaussian-Elimination Decoding",
  "title_text": "Chordal Codes: Code Construction and Efficient Gaussian-Elimination Decoding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/7arz4kjkk501z",
  "venue": "arXiv",
  "versions": []
}