{
  "abstract": "Evolutionary program search driven by large language models (LLMs) has produced record-breaking constructions for open problems in combinatorics and beyond. We apply this approach to the longstanding problem of improving the best-known bounds for binary linear codes. Building on the EvoTune evolutionary framework and the ShinkaEvolve codebase, we introduce LinCodeEvolve, which evolves code-construction programs against an exact minimum-distance evaluator. A strategy loop combines diversity-driven search and expert supervision: when progress plateaus, new strategies are used to redirect the search. LinCodeEvolve discovers seven record-breaking codes, $[172,21,66]$, $[173,20,68]$, $[176,21,68]$, $[181,21,70]$, $[184,21,72]$, $[189,22,72]$ and $[200,21,77]$, six of which have concise quasi-cyclic descriptions. With standard code modification techniques, they improve $22$ entries of the tables. Every code is verified by exhaustive enumeration. These results suggest that LLM-guided search can help find improved codes and complement existing methods in coding theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37056",
  "author_total": 4,
  "authors": [
    {
      "name": "Amal Seddas"
    },
    {
      "name": "Vladyslav Shashkov"
    },
    {
      "name": "Maryna Viazovska"
    },
    {
      "name": "Emmanuel Abbe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dh021ntpdc55p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37056",
  "fulltext_url": null,
  "id": "dh021ntpdc55p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37056",
  "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.NE"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7214898835",
  "pdf_url": "https://arxiv.org/pdf/2609.37056",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dh021ntpdc55p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37056",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37056"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes",
  "title_text": "Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/dh021ntpdc55p",
  "venue": "arXiv",
  "versions": []
}