{
  "abstract": "We prove the nonexistence of eight circulant weighing matrices from the remaining table of orders at most $200$ and weights at most $100$. The proofs combine contraction, character evaluation on the kernel of a contraction, multiplier methods, and exact finite computations. For $CW(105,36)$, the contracted matrix is unique up to equivalence. Applying a nonprincipal character of the $C_3$ kernel gives an element over the Eisenstein integers; reduction modulo $1-ω$ gives a word in a ternary cyclic code of length $35$, and exact enumeration rules out every required Eisenstein-unit lift. For $CW(140,36)$, the real-valued character $Y\\mapsto-1$ of the $C_4$ kernel is incompatible with the same contracted class. For weight $64$, the faithful character $Y\\mapsto i$ of a $C_4$ kernel first gives an element of $\\mathbb{Z}[i][C_m]$; a generalized multiplier then forces constancy on multiplication-by-$2$ orbits, and exact correlation calculations eliminate orders $140$, $180$, and $196$. The three weight-$49$ cases are settled by the ordinary prime-power multiplier, with contraction where needed. Consequently none of $CW(105,36)$, $CW(140,36)$, $CW(116,49)$, $CW(120,49)$, $CW(192,49)$, $CW(140,64)$, $CW(180,64)$, and $CW(196,64)$ exists.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18468",
  "author_total": 1,
  "authors": [
    {
      "name": "Ming Ming Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/139yv3wd4ygsm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18468",
  "fulltext_url": null,
  "id": "139yv3wd4ygsm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18468",
  "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.RA"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7203939405",
  "pdf_url": "https://arxiv.org/pdf/2608.18468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/139yv3wd4ygsm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2608.18468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Character and Multiplier Obstructions for Circulant Weighing Matrices",
  "title_text": "Character and Multiplier Obstructions for Circulant Weighing Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/139yv3wd4ygsm",
  "venue": "arXiv",
  "versions": []
}