{
  "abstract": "We study the variation of hull dimensions of symplectic linear codes under equivalence transformations preserving the symplectic distance. For a symplectic linear code $C$, we introduce an even-valued invariant $Δ(C)$, which depends only on the equivalence class of $C$. This invariant can be expressed as the generic rank of an associated space of alternating matrices and, equivalently, as twice a corresponding matroid matching number. If $C$ has dimension $k$, we prove that the minimum symplectic hull dimension among all codes equivalent to $C$ is $k-Δ(C)$. Consequently, $C$ is equivalent to a symplectic LCD code if and only if $Δ(C)=k$. We further show that every symplectic MDS code of even dimension is monomially equivalent to a symplectic LCD code. For a symplectic self-orthogonal code $C$, we determine all attainable hull dimensions: for every integer $r$ with $0\\le r\\le Δ(C)/2$, there exists a monomially equivalent code whose symplectic hull has dimension $k-2r$. We also refine a standard form for the generator matrix of a symplectic self-orthogonal code and derive the corresponding parity-check matrix and the Gram matrix of the dual code. In the self-dual case, we characterize $Δ(C)$ through minors of an associated symmetric matrix. Furthermore, we relate hull variation to graph matchings, establish a bound for $Δ(C)$, and give graph constructions producing symplectic self-dual MDS, optimal, and best-known codes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15535",
  "author_total": 3,
  "authors": [
    {
      "name": "Kanat Abdukhalikov"
    },
    {
      "name": "Somi Gupta"
    },
    {
      "name": "Duy Ho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/775mkke8ezmpm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15535",
  "fulltext_url": null,
  "id": "775mkke8ezmpm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15535",
  "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.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7221794604",
  "pdf_url": "https://arxiv.org/pdf/2610.15535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/775mkke8ezmpm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hull Variation in Symplectic Linear Codes",
  "title_text": "Hull Variation in Symplectic Linear Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/775mkke8ezmpm",
  "venue": "arXiv",
  "versions": []
}