{
  "abstract": "We study the problem of finding shortest self-orthogonal embeddings of a given code which have the largest possible minimum distance by employing a constraint-preserving genetic algorithm. We show that the orthogonal group is generated by transvections corresponding to weight-four vectors. Using this result together with the fact that all shortest self-orthogonal embeddings can be obtained through the action of the orthogonal group, we construct a genetic algorithm in which each chromosome is represented by a sequence of weight-four vectors. Applying our algorithm to codes with dimensions $9\\le k\\le 15$ and lengths $22\\le n\\le 256$, we obtain 280 inequivalent optimal self-orthogonal codes. In particular, we obtain 34 codes with new parameters and 100 codes which are inequivalent to previously known codes with the same parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02135",
  "author_total": 3,
  "authors": [
    {
      "name": "Haeun Lim"
    },
    {
      "name": "Junmin An"
    },
    {
      "name": "Jon-Lark Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dyyzmvhxy3sj3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02135",
  "fulltext_url": null,
  "id": "dyyzmvhxy3sj3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02135",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7207643573",
  "pdf_url": "https://arxiv.org/pdf/2609.02135",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dyyzmvhxy3sj3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.02135",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02135"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Embedding Linear Codes into Optimal Self-Orthogonal Codes Based on Constraint-Preserving Genetic Algorithms",
  "title_text": "Embedding Linear Codes into Optimal Self-Orthogonal Codes Based on Constraint-Preserving Genetic Algorithms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/dyyzmvhxy3sj3",
  "venue": "arXiv",
  "versions": []
}