{
  "abstract": "In this article, we consider a special class of Williamson type matrices which we call them near Williamson matrices. They are in fact four $n\\times n$ $(-1, 1)$-matrices $A, B, C, D$ so that $A$ is circulant, $B,C,D$ are symmetric circulant, and they satisfy $AA^\\top+BB^\\top+CC^\\top+DD^\\top=4nI$. Using a computer search, we find all inequivalent near Williamson matrices for all odd orders at most $35$. We also show that such matrices exist for all odd orders up to $63$. As a consequence, we find the first known example of a quaternary Hadamard matrix of order $118$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.08661",
  "author_total": 3,
  "authors": [
    {
      "name": "Hadi Kharaghani"
    },
    {
      "name": "Ali Mohammadian"
    },
    {
      "name": "Behruz Tayfeh-Rezaie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32n9734wn9sm5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.08661",
  "fulltext_url": null,
  "id": "32n9734wn9sm5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.08661",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7160925344",
  "pdf_url": "https://arxiv.org/pdf/2605.08661",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32n9734wn9sm5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2605.08661",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.08661"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A search for Hadamard matrices of Williamson type",
  "title_text": "A search for Hadamard matrices of Williamson type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/32n9734wn9sm5",
  "venue": "arXiv",
  "versions": []
}