{
  "abstract": "A pseudorandom code (PRC) is a keyed error-correcting code whose codewords are computationally indistinguishable from uniform strings. We study public-key PRCs over fixed alphabets against adversarial deletions, where the deletion channel may both depend on the public encoding key and the transmitted codeword. Let $γ_q^{\\mathrm{LCS}}$ denote the asymptotic normalised longest-common-subsequence length of two independent uniform $q$-ary strings. We prove that for every fixed $q\\ge2$ no multi-message public-key PRC with a single-output decoder is robust against all such $δ$-deletion channels for any $δ>1-γ_q^{\\mathrm{LCS}}$. For $q=2$, the current rigorous bound $γ_2\\ge0.792665992$ rules out every constant $δ>0.207334008$. The proof uses pseudorandomness only to transfer an LCS event from uniform strings to independently sampled codewords and therefore also the resulting collision argument is information-theoretic and requires no secret key. We also extend the argument to list decoding: for every fixed constant $L$, provided the message space contains at least $L+1$ messages, no such PRC with output lists of size at most $L$ is robust for $δ>1-γ_2^{(L+1)}$. Since $γ_2^{(m)}=1/2+Θ(1/\\sqrt m)$, these thresholds approach $1/2$. Our bounds are specific to public-key-dependent adversarial channels and do not apply to oblivious edit channels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02943",
  "author_total": 2,
  "authors": [
    {
      "name": "Frederick Dehmel"
    },
    {
      "name": "Shilun Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cm3azwhedkxqb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02943",
  "fulltext_url": null,
  "id": "cm3azwhedkxqb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02943",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CR"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7208772038",
  "pdf_url": "https://arxiv.org/pdf/2609.02943",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cm3azwhedkxqb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.02943",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02943"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "A Public-Key-Dependent Adversarial-Deletion Ceiling for Fixed-Alphabet Multi-Bit Pseudorandom Codes",
  "title_text": "A Public-Key-Dependent Adversarial-Deletion Ceiling for Fixed-Alphabet Multi-Bit Pseudorandom Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/cm3azwhedkxqb",
  "venue": "arXiv",
  "versions": []
}