{
  "abstract": "Levenshtein's classical theorem shows that any code that can uniquely decode from \\(t\\) deletions can also uniquely decode from \\(t\\) insertions. This symmetry, however, does not generally hold in the list-decoding regime. Several prior results on the capacity and radii of list-decoding from insertions and deletions suggest that insertions are easier to handle than deletions. In an effort to better understand this asymmetry between insertions and deletions under list-decoding, we study an analogous version of McEliece's \\emph{average list size problem}. More precisely, given a binary code \\(\\mathcal{C}\\) of length \\(n\\) that uniquely corrects \\(t'\\) insertions (or deletions), we are interested in the average number of codewords returned by a \\(t\\)-insertion (or deletion) list decoder, where \\(t' < t\\). Focusing on the case of \\(t'=1\\) and \\(t=2\\), we find that under two insertions, this quantity is at most \\((n+12)/4\\) for any VT code of length \\(n\\), whereas under two deletions it is at least \\(n/2 - 10\\) when averaged over all length-\\(n\\) VT codes. The nearly factor-of-two gap between these upper and lower bounds serves to confirm the relative ease of list-decoding of insertions compared to deletions from an average-case perspective.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15767",
  "author_total": 4,
  "authors": [
    {
      "name": "Anisha Banerjee"
    },
    {
      "name": "Roni Con"
    },
    {
      "name": "Antonia Wachter-Zeh"
    },
    {
      "name": "Eitan Yaakobi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ba2xw56j3czav.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15767",
  "fulltext_url": null,
  "id": "ba2xw56j3czav",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15767",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7221831079",
  "pdf_url": "https://arxiv.org/pdf/2610.15767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ba2xw56j3czav.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15767"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "On the Average List Size of VT Codes under Two Insertions or Two Deletions",
  "title_text": "On the Average List Size of VT Codes under Two Insertions or Two Deletions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ba2xw56j3czav",
  "venue": "arXiv",
  "versions": []
}