{
  "abstract": "LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we develop a local-growth argument for estimating ball sizes in the coset graphs of LDPC codes. Rather than estimating coset balls directly, we use a local-growth analysis to bound the coset-weight generating function of linear spaces spanned by low-weight vectors. This approach sharpens the previous ball-size estimates of Iceland and Samorodnitsky. Combined with a general method of Friedman and Tillich that relates balls in coset graphs to sizes of error-correcting codes, it further improves the upper bounds on the rate of LDPC codes for a significant range of relative distances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.01213",
  "author_total": 2,
  "authors": [
    {
      "name": "Chong Shangguan"
    },
    {
      "name": "Yulin Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e5k28k5dnvgfc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.01213",
  "fulltext_url": null,
  "id": "e5k28k5dnvgfc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.01213",
  "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.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1705|Error Correcting Code Techniques"
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  "openalex": "W7160241212",
  "pdf_url": "https://arxiv.org/pdf/2605.01213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e5k28k5dnvgfc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2605.01213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.01213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Improved Rate-versus-Distance Upper Bounds for LDPC Codes",
  "title_text": "Improved Rate-versus-Distance Upper Bounds for LDPC Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/e5k28k5dnvgfc",
  "venue": "arXiv",
  "versions": []
}