{
  "abstract": "Does there exist an 8-variable balanced Boolean function with nonlinearity 118? This is a famous and long-standing open problem in Boolean functions. In this paper, we give a negative answer to this open problem, and prove that the maximum nonlinearity of balanced Boolean functions in 8 variables is 116, establishing the 8-variable instance of Dobbertin's conjectured recursion for the minimum Walsh peak of balanced functions. Equivalently, the covering radius of the Reed--Muller code RM(1,8) in 0-resilient Boolean functions is 116. We deduce the result by obtaining a quadratic form of polar rank 6, and reducing the problem to the existence of a 6-variable Boolean function with nonlinearity greater than 26 whose Hamming distance to a bent function is between 4 and 6.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17897",
  "author_total": 3,
  "authors": [
    {
      "name": "Yueying Lou"
    },
    {
      "name": "Youle Xu"
    },
    {
      "name": "Qichun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/69dh63bxjq50n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17897",
  "fulltext_url": null,
  "id": "69dh63bxjq50n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17897",
  "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.CR"
    ],
    [
      "arxiv",
      "cs.IT"
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    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
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  "openalex": "W7221828114",
  "pdf_url": "https://arxiv.org/pdf/2610.17897",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/69dh63bxjq50n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.17897",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17897"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "The Maximum Nonlinearity of 8-variable Balanced Boolean Functions is 116",
  "title_text": "The Maximum Nonlinearity of 8-variable Balanced Boolean Functions is 116",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/69dh63bxjq50n",
  "venue": "arXiv",
  "versions": []
}