{
  "abstract": "We introduce and study Reed--Solomon sunflowers, namely families of Reed--Solomon codes whose pairwise intersections are all equal to the same fixed subspace. This notion lies at the intersection of extremal subspace combinatorics and coding theory: it can be viewed as a structured version of the sunflower problem in the Grassmannian, and it naturally produces constant-dimension subspace codes with prescribed minimum distance. We focus mainly on the case in which the center is the one-dimensional space generated by the all-one vector. We give an algebraic criterion, expressed in terms of generalized $V$-matrices, ensuring that a family of Reed--Solomon codes forms such a sunflower. We then study the size of these families through counting and constructions. In dimension two, we show that all distinct Reed--Solomon codes form a sunflower and determine its size by counting Reed--Solomon codes up to affine equivalence of their evaluation vectors. For fixed dimension $k\\geq3$ and length $\\ell\\geq2k-1$, we give an explicit recursive construction with $Ω_{k,\\ell}(q^{\\lfloor\\ell/(2k-1)\\rfloor})$ petals and a greedy existence argument with $Ω_{k,\\ell}(q^{\\ell-2k+2})$ petals as $q\\to\\infty$. We also apply the greedy argument to obtain families of $[\\ell,k]_q$ MDS codes of size $Ω_{k,\\ell}(q^{2(\\ell-2k+2)})$, whose pairwise intersections have dimension at most one but need not be equal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33512",
  "author_total": 4,
  "authors": [
    {
      "name": "Roni Con"
    },
    {
      "name": "Anina Gruica"
    },
    {
      "name": "Maria Montanucci"
    },
    {
      "name": "Ferdinando Zullo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38dyqbax47aw6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33512",
  "fulltext_url": null,
  "id": "38dyqbax47aw6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33512",
  "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.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7214778990",
  "pdf_url": "https://arxiv.org/pdf/2609.33512",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38dyqbax47aw6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.33512",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33512"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sunflowers of Reed--Solomon Codes",
  "title_text": "Sunflowers of Reed--Solomon Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/38dyqbax47aw6",
  "venue": "arXiv",
  "versions": []
}