{
  "abstract": "We consider the problem of binary sequence reconstruction where a sequence is transmitted multiple times over a channel, and each undergoes substitution errors by an arbitrary error vector of Hamming weight exactly $t$. We determine $N_{\\mathrm{wc}}$, the minimum number of distinct channel output observations guaranteeing unique reconstruction by an optimal decoder, and show that the bit-wise majority-vote decoder, which was proved by Levenshtein (2001) to be optimal for channels corrupting up to $t$ bits, is in fact suboptimal here. Despite this suboptimality, we prove a condition that admits a practical early-termination rule, necessary for every decoder at any number of outputs $N$, and sufficient for bit-wise majority-vote even below $N_{\\mathrm{wc}}$. We evaluate the number of outputs at which this condition is triggered, numerically, and show that it frequently occurs below $N_{\\mathrm{wc}}$ when the block-length $k>2t+1$. Finally, we propose an alternative algorithm aimed at guaranteeing unique reconstruction with fewer observations than bit-wise majority-vote, and demonstrate through exhaustive enumeration that it successfully decodes channel output-sets where bit-wise majority-vote fails.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30001",
  "author_total": 4,
  "authors": [
    {
      "name": "Vivian Papadopoulou"
    },
    {
      "name": "Yonatan Yehezkeally"
    },
    {
      "name": "V. Arvind Rameshwar"
    },
    {
      "name": "Antonia Wachter-Zeh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c780spr87jvpj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30001",
  "fulltext_url": null,
  "id": "c780spr87jvpj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30001",
  "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": "W7223225960",
  "pdf_url": "https://arxiv.org/pdf/2610.30001",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c780spr87jvpj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.30001",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30001"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "When Majority-Vote Fails: Sequence Reconstruction under Fixed-Weight Substitutions",
  "title_text": "When Majority-Vote Fails: Sequence Reconstruction under Fixed-Weight Substitutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/c780spr87jvpj",
  "venue": "arXiv",
  "versions": []
}