{
  "abstract": "Bent partitions play a significant role in the theory of bent functions. In this paper, we study weakly regular bent partitions, that is, all generated bent functions are weakly regular (called in class $\\mathcal{WRBP}$). Let $Γ=\\{A_{i}, i \\in V_{m}\\}$ be a bent partition of $V_{n}$ in class $\\mathcal{WRBP}$, where $V_{n}$ denotes an $n$-dimensional vector space over the prime field $\\mathbb{F}_{p}$, $n$ is even, $m \\leq \\frac{n}{2}$, and $m \\geq 2$ if $p=2$. We first characterize bent partition $Γ$ in terms of the duals of component functions of vectorial bent functions. In particular, we prove that if $p \\neq 3$, then all bent functions generated by $Γ$ are regular. Building on the above result, we give characterizations of bent partition $Γ$ in terms of two classes of linear codes. When $n \\geq 4$ and $m=\\frac{n}{2}$, except for the case where $(p, n)=(2, 4)$ and $|A_{i_{0}}|=1$ for some $i_{0}$, we show that $Γ$ is obtained from a spread (after a shift). Particularly, any normal bent partition of $V_{n}$ of depth $p^{\\frac{n}{2}}$ in class $\\mathcal{WRBP}$ must be obtained from a spread (after a shift), where $n \\geq 4$. We establish the Macwilliams-like identities for bent partitions in class $\\mathcal{WRBP}$. Furthermore, if $p$ is odd, we present some nonexistence results on bent partitions in class $\\mathcal{WRBP}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41779",
  "author_total": 5,
  "authors": [
    {
      "name": "Jiaxin Wang"
    },
    {
      "name": "Yadi Wei"
    },
    {
      "name": "Fang-Wei Fu"
    },
    {
      "name": "Jin Li"
    },
    {
      "name": "Fulin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bj8rmrbdjgwr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41779",
  "fulltext_url": null,
  "id": "8bj8rmrbdjgwr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41779",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41779",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bj8rmrbdjgwr.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41779",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41779"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Characterizations and MacWilliams-Like Identities of Weakly Regular Bent Partitions",
  "title_text": "Characterizations and MacWilliams-Like Identities of Weakly Regular Bent Partitions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/8bj8rmrbdjgwr",
  "venue": "arXiv",
  "versions": []
}