{
  "abstract": "We spent five weeks using an LLM coding agent on open problems in coding theory: finding large sets of four-letter words, such as DNA barcodes, that stay far apart in edit distance. The agent wrote the verifiers and search code; a human chose the problem and set the verification protocol. Restricting the search to codes with a prescribed symmetry, a classical technique, shrank the problem about fourfold and raised the best known code of length 6 and minimum edit distance 3 from 114 to 120 words ($E_4(6,3) \\geq 120$). The same pipeline improved twelve further lower bounds at lengths 6 to 9 and distances 3 to 6. We give the failures equal space. Our own search stopped at 116 and recorded the last symmetry class as topping out at 112; a second agent session, running the same search with a better operator, found the 120. A later verdict that the method did not carry over to length 7 was wrong for the same reason, and an earlier instance cost three weeks. Each time, an intermediate result was written down, never rechecked, and treated as a fact that ruled out further search. Checking final outputs, as our protocol required, does not catch such errors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39081",
  "author_total": 1,
  "authors": [
    {
      "name": "Abraham Yeung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78fdp9q26nt5z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39081",
  "fulltext_url": null,
  "id": "78fdp9q26nt5z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39081",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7215092940",
  "pdf_url": "https://arxiv.org/pdf/2609.39081",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78fdp9q26nt5z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39081",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39081"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Coding Agents for Coding Theory",
  "title_text": "Coding Agents for Coding Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/78fdp9q26nt5z",
  "venue": "arXiv",
  "versions": []
}