{
  "abstract": "This paper investigates the construction of full-systematic permutation codes capable of correcting multiple deletions under two complementary models, namely symbol-invariant deletions (SIDs), where surviving symbol values are preserved, and permutation-invariant deletions (PIDs), where the surviving sequence is standardized to a permutation. For any fixed integer $t \\ge 1$ and all sufficiently large message lengths $n$, our proposed encoders map any message permutation of length $n$ to a codeword by inserting distinct redundancy symbols while strictly preserving the sequence order of the original message symbols. The proposed constructions correct up to $t$ deletions using $7t-1$ redundancy markers for PIDs and $4t$ redundancy markers for SIDs, achieving redundancies of $(7t-1)\\log n + O_t(1)$ bits and $4t\\log n + O_t(1)$ bits, respectively. Both code families are uniformly constructible, encodable, and decodable in $n^{O(t)}$ time. The underlying framework stores an inner deletion-correcting syndrome in the relative positions of redundancy markers via an algebraic outer code based on integer moments and residual graph coloring. We further extend this framework to fixed-composition and strictly $λ$-regular multipermutations, proving that the PID and SID channels coincide whenever the common multiplicity satisfies $λ> t$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37578",
  "author_total": 5,
  "authors": [
    {
      "name": "Bolin Wu"
    },
    {
      "name": "Quan D. Bui"
    },
    {
      "name": "Kai Niu"
    },
    {
      "name": "Van Khu Vu"
    },
    {
      "name": "Shuche Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/217n6mrjfnw3p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37578",
  "fulltext_url": null,
  "id": "217n6mrjfnw3p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37578",
  "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": "W7214890007",
  "pdf_url": "https://arxiv.org/pdf/2609.37578",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/217n6mrjfnw3p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37578",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37578"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Order-Optimal Systematic Permutation Codes for Correcting t Deletions",
  "title_text": "Order-Optimal Systematic Permutation Codes for Correcting t Deletions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/217n6mrjfnw3p",
  "venue": "arXiv",
  "versions": []
}