{
  "abstract": "Bent functions are Boolean functions in an even number of variables that are indicators of Hadamard difference sets in elementary abelian 2-groups. A bent functionfinmvariables is said to be normal if it is constant on an affine space of dimensionm/2. In this paper, we demonstrate that all bent functions in m = 8 variables, whose exact count, determined by Langevin and Leander (Des. Codes Cryptogr. 59(1–3): 193–205, 2011), is approximately 2106, share a common algebraic property: every 8-variable bent function is normal, up to the addition of a linear function. With this result, we complete the analysis of the normality of bent functions for the last unresolved case,m= 8. It is already known that all bent functions inmvariables are normal form≤ 6, while form≥ 10, there exist bent functions that cannot be made normal by adding linear functions. Consequently, we provide a complete solution to an open problem by Charpin (J. Complex. 20(2-3): 245-265, 2004).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Valérie Gillot"
    },
    {
      "name": "Philippe Langevin"
    },
    {
      "name": "Alexandr Polujan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/795s1qc8es9vd.bib",
  "cited_by": 0,
  "doi": "10.1109/tit.2026.3685370",
  "fulltext_url": null,
  "id": "795s1qc8es9vd",
  "issns": [
    "0018-9448"
  ],
  "landing_url": "https://hal.science/hal-05774356v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7154946908",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": "Institute of Electrical and Electronics Engineers",
  "ris": "https://research.draconitic.com/paper/795s1qc8es9vd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:45Z",
      "native_id": "hal-05774356",
      "source": "hal",
      "url": "https://hal.science/hal-05774356v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Normality of 8-bit Bent Functions",
  "title_text": "Normality of 8-bit Bent Functions",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:45Z",
  "url": "https://research.draconitic.com/paper/795s1qc8es9vd",
  "venue": "IEEE Transactions on Information Theory",
  "versions": []
}