{
  "abstract": "Affine Grassmann codes, introduced by Beelen, Ghorpade and Høholdt, are linear codes over $\\mathbb{F}_q$ obtained by evaluating linear combinations of minors of a generic matrix. The weight spectrum of the affine Grassmann code $C^{\\mathbb{A}}(2,m)$ was determined by Piñero and Singh via a case analysis on the rank of an associated alternating matrix. We give an independent and more streamlined derivation, valid for all $m\\ge4$ and every prime power $q$, in which each codeword is written in a compact matrix form and its Hamming weight is expressed through a single closed formula involving two explicit affine subspaces and their intersection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10274",
  "author_total": 1,
  "authors": [
    {
      "name": "Rohit Yadav"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0b0ak5memgj16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10274",
  "fulltext_url": null,
  "id": "0b0ak5memgj16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10274",
  "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": "W7212126167",
  "pdf_url": "https://arxiv.org/pdf/2609.10274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0b0ak5memgj16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Revisiting the Weight Spectrum of the Affine Grassmann Code $C^{\\mathbb{A}}(2,m)$",
  "title_text": "Revisiting the Weight Spectrum of the Affine Grassmann Code C^𝔸(2,m)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/0b0ak5memgj16",
  "venue": "arXiv",
  "versions": []
}