{
  "abstract": "The Hadamard maximal determinant problem seeks an $n\\times n$ matrix $X$ with entries in $\\{\\pm 1\\}$, which maximizes the determinant $\\vert \\det X \\vert$ for a given order $n \\in \\mathbb{N}$. We report matrices attaining new record determinants for orders $n\\equiv 3\\pmod{4}$ between $103$ and $119$, as well as $n=51$. We provide a proof of optimality within a specific family of circulant--block constructions for $X$. For these orders, we recast the Hadamard problem as a sequence reconstruction problem from a pair of periodic autocorrelation functions, subject to certain arithmetic conditions. We describe several learning--based strategies for reconstruction and provide a comparison with classical simulated annealing--style approaches as a benchmark.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22518",
  "author_total": 9,
  "authors": [
    {
      "name": "Giorgi Butbaia"
    },
    {
      "name": "Justin Tan"
    },
    {
      "name": "Pragatheeswaran Vipulanandan"
    },
    {
      "name": "Xiaoyu Huang"
    },
    {
      "name": "Toby Saunders-A'Court"
    },
    {
      "name": "Lucas Fagan"
    },
    {
      "name": "Davide Passaro"
    },
    {
      "name": "Michele Tarquini"
    },
    {
      "name": "Sergei Gukov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6rjcxp7twz16a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22518",
  "fulltext_url": null,
  "id": "6rjcxp7twz16a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22518",
  "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.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7203858596",
  "pdf_url": "https://arxiv.org/pdf/2608.22518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6rjcxp7twz16a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2608.22518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22518"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "New Records for the Hadamard Maximal Determinant Problem",
  "title_text": "New Records for the Hadamard Maximal Determinant Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/6rjcxp7twz16a",
  "venue": "arXiv",
  "versions": []
}