{
  "abstract": "We develop q-ary Guessing Random Additive Noise Decoding (GRAND) for linear codes over a q-ary alphabet. The decoder works on a sorted symbol-likelihood array and uses three local child generation rules to generate symbol deviation patterns. We then prove that these rules induce a monotone rooted spanning tree of the full row-index space, so best-first traversal gives maximum-likelihood (ML) decoding under unlimited search. Reed-Solomon simulations verify ML agreement and show the finite-budget performance-complexity tradeoff.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10236",
  "author_total": 3,
  "authors": [
    {
      "name": "Reza Dianat"
    },
    {
      "name": "Majid Nasiri Khormuji"
    },
    {
      "name": "Hiroyuki Seki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj2z091z04ew6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10236",
  "fulltext_url": null,
  "id": "bj2z091z04ew6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10236",
  "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": "W7220961187",
  "pdf_url": "https://arxiv.org/pdf/2610.10236",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj2z091z04ew6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10236",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10236"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "q-ary GRAND",
  "title_text": "q-ary GRAND",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/bj2z091z04ew6",
  "venue": "arXiv",
  "versions": []
}