{
  "abstract": "We study external difference families arising from cyclotomic classes in finite fields from the viewpoint of a fixed number of blocks. For families consisting of even-indexed cyclotomic classes, the EDF condition can be expressed in terms of relations among cyclotomic numbers. We first study the two-block case and recover a classical characterization in terms of quadratic forms. Our main result shows that, for a prime $p=12k+1$, the family $\\{C_0^6,C_2^6,C_4^6\\}$ forms an EDF in $\\mathbb{F}_p$ if and only if $k$ is a square. The proofs combine symmetry relations of cyclotomic numbers with their explicit evaluations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07266",
  "author_total": 2,
  "authors": [
    {
      "name": "Miwako Mishima"
    },
    {
      "name": "Yu Tsunoda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85j1x3j9eepew.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07266",
  "fulltext_url": null,
  "id": "85j1x3j9eepew",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07266",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7212017029",
  "pdf_url": "https://arxiv.org/pdf/2609.07266",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85j1x3j9eepew.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07266",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07266"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "External Difference Families Arising from Two or Three Cyclotomic Classes",
  "title_text": "External Difference Families Arising from Two or Three Cyclotomic Classes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/85j1x3j9eepew",
  "venue": "arXiv",
  "versions": []
}