{
  "abstract": "We prove that for every prime power $q$ and every $p \\in (0, 1-1/q)$, a random $\\mathbb{F}_q$-linear code of rate $1 - h_q(p) - ε$ is $(p, C_{p,q}/ε)$-average-radius list-decodable with probability at least $1 - q^{-Ω(n)}$, i.e., for every center $y \\in \\mathbb{F}_q^n$, the $C_{p,q}/ε$ codewords closest to $y$ have average fractional Hamming distance at least $p$ from $y$. This extends a similar result for (standard) list-decoding due to Guruswami, Håstad, and Kopparty (2010) to the stronger average-radius guarantee, with the same $O(1/ε)$ list size. For average-radius list-decoding, such a result was previously known only for binary linear codes (Guruswami, Li, Mosheiff, Resch, Silas, and Wootters, 2021) and for general (non-linear) random codes over arbitrary alphabets (Elias, 1991).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22663",
  "author_total": 3,
  "authors": [
    {
      "name": "Venkatesan Guruswami"
    },
    {
      "name": "Shilun Li"
    },
    {
      "name": "Mihir Singhal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tzfnzhzppy2y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22663",
  "fulltext_url": null,
  "id": "8tzfnzhzppy2y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22663",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7204155351",
  "pdf_url": "https://arxiv.org/pdf/2608.22663",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tzfnzhzppy2y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.22663",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22663"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Average-Radius List-Decodability of Random Linear Codes",
  "title_text": "Average-Radius List-Decodability of Random Linear Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8tzfnzhzppy2y",
  "venue": "arXiv",
  "versions": []
}