{
  "abstract": "It is well known that the sum of two bent functions on $\\mathbb{F}^n$ has algebraic degree at most $n/2$ for even $n\\ge 4$. Tokareva conjectured that the converse holds: every Boolean function with degree at most $n/2$ can be written as a sum of two bent functions. The conjecture has been verified for even $n\\leq 6$ and for several special classes of Boolean functions. We disprove this conjecture by showing that $x_1x_2(x_3x_4+x_5x_6+x_7x_8)$ is not a sum of two bent functions on $\\mathbb{F}^8$. We extend this construction to obtain counterexamples in every even dimension $n\\ge 8$. Using Shaporenko's reduction, we also obtain explicit counterexamples to Tokareva's derivative conjecture in every even dimension $n\\ge 10$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32239",
  "author_total": 5,
  "authors": [
    {
      "name": "Yansong Feng"
    },
    {
      "name": "Hao Jiang"
    },
    {
      "name": "Guancheng Li"
    },
    {
      "name": "Tianyi Li"
    },
    {
      "name": "Lili Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ynr0rpqeyrt4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32239",
  "fulltext_url": null,
  "id": "1ynr0rpqeyrt4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32239",
  "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.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7223659922",
  "pdf_url": "https://arxiv.org/pdf/2610.32239",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ynr0rpqeyrt4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32239",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32239"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A counterexample to Tokareva's conjecture on sums of two bent functions",
  "title_text": "A counterexample to Tokareva's conjecture on sums of two bent functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/1ynr0rpqeyrt4",
  "venue": "arXiv",
  "versions": []
}