{
  "abstract": "We complete the determination of the minimum possible length of eight-dimensional binary self-orthogonal codes with given minimum distance. For dimension nine we give exact values and bounds for minimum distance at most $64$. By exploiting the geometric reformulation of linear codes as multisets of points, we fully redo the classification for dimension at most seven in a simplified and computer-free manner. As a by-product we prove the non-existence of $[93,9,44]_2$ codes and show several divisibility results for putative optimal nine-dimensional binary codes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39870",
  "author_total": 1,
  "authors": [
    {
      "name": "Sascha Kurz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b296m6891r4h9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39870",
  "fulltext_url": null,
  "id": "b296m6891r4h9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39870",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
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      "arxiv",
      "cs.IT"
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      "arxiv",
      "math.CO"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39870",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b296m6891r4h9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39870",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39870"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Optimal self-orthogonal binary linear codes",
  "title_text": "Optimal self-orthogonal binary linear codes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/b296m6891r4h9",
  "venue": "arXiv",
  "versions": []
}