{
  "abstract": "In this article, we consider the affine Grassmann code $C^{\\mathbb A}(3,6)$, obtained from the affine open cell ${\\mathbb A}^9$ of the Grassmannian $G_{3,6}$. We exploit the representation of codewords as linear combinations of minors of all sizes of a generic $3\\times3$ matrix and classify them according to the largest size of a minor occurring with a nonzero coefficient. Using this classification, we determine all possible Hamming weights of codewords of $C^{\\mathbb A}(3,6)$ and, for each weight, compute the number of codewords attaining that weight. Consequently, we obtain the complete weight spectrum of the affine Grassmann code $C^{\\mathbb A}(3,6)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08784",
  "author_total": 2,
  "authors": [
    {
      "name": "Prasant Singh"
    },
    {
      "name": "Rohit Yadav"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22yz3kxhc8w2m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08784",
  "fulltext_url": null,
  "id": "22yz3kxhc8w2m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08784",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7212017002",
  "pdf_url": "https://arxiv.org/pdf/2609.08784",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22yz3kxhc8w2m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2609.08784",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08784"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "The Weight Spectrum of the Affine Grassmann Code $C^{\\mathbb A}(3,6)$",
  "title_text": "The Weight Spectrum of the Affine Grassmann Code C^𝔸(3,6)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/22yz3kxhc8w2m",
  "venue": "arXiv",
  "versions": []
}