{
  "abstract": "The purpose of this paper is to investigate the self-orthogonal embedding problem for linear codes over Z4. We propose several tight bounds on the length of the shortest self-orthogonal embedding over Z4, and determine the exact shortest self-orthogonal embedding length under specific conditions. As an example satisfying these conditions, we establish the exact length of the shortest self-orthogonal embedding for the quaternary Preparata codes. Furthermore, to establish these results, we completely classify the exact length of the shortest doubly even self-orthogonal embedding for binary linear codes in every possible case. Finally, when the shortest self-orthogonal embedding length of a given free code over Z4 is equal to the shortest doubly even self-orthogonal embedding length of its residue code, we present an algorithm to construct all possible shortest self-orthogonal embeddings. With our algorithm, we found twelve linear codes over Z4 whose minimum Lee distances are higher than those of the Z4-linear codes in Aydins database.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.08964",
  "author_total": 3,
  "authors": [
    {
      "name": "Junmin An"
    },
    {
      "name": "Jon-Lark Kim"
    },
    {
      "name": "San Ling"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4sprr6kyp44ta.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.08964",
  "fulltext_url": null,
  "id": "4sprr6kyp44ta",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.08964",
  "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": "W7163984496",
  "pdf_url": "https://arxiv.org/pdf/2606.08964",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4sprr6kyp44ta.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2606.08964",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.08964"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Embedding linear codes over Z4 into self-orthogonal codes",
  "title_text": "Embedding linear codes over Z4 into self-orthogonal codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/4sprr6kyp44ta",
  "venue": "arXiv",
  "versions": []
}