{
  "abstract": "This paper studies when list-decodability guarantees for error-correcting codes of good distance can go beyond the classical Johnson radius and gives a corresponding efficient list-decoding algorithm for Reed-Solomon codes up to this new radius. The Johnson bound shows that any error-correcting code with distance $δ$ is automatically list-decodable with small list size up to a certain radius $J(δ)$ around any received word $r$. We show that if the received word $r$ is known to have some codewords that are somewhat close to it (we call these ``hints\"), then $C$ is list-decodable with small list size up to an even larger radius around $r$. We determine the optimal list-decoding radius in this setting for single and multiple hints over both large and small alphabets and show that this radius is the optimum of a natural convex program. Remarkably, even a single hint that is $(J(δ)-ε)$-close to $r$ improves the list-decoding radius around $r$ to $J(δ)+ε'$. Finally, we give an efficient algorithm, based on the weighted Guruswami-Sudan decoder, that list-decodes Reed-Solomon codes up to this optimal radius.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38022",
  "author_total": 2,
  "authors": [
    {
      "name": "Swastik Kopparty"
    },
    {
      "name": "Harry Sha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80c2j7bredg23.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38022",
  "fulltext_url": null,
  "id": "80c2j7bredg23",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38022",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80c2j7bredg23.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38022"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "An Improved Johnson Bound for List-Decoding with Hints",
  "title_text": "An Improved Johnson Bound for List-Decoding with Hints",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/80c2j7bredg23",
  "venue": "arXiv",
  "versions": []
}