{
  "abstract": "In this paper, we give a classification of the minimum weight codewords of Schubert codes $C_α(\\ell, m)$ by settling the conjecture proposed by Ghorpade and Singh in 2018, for all values of $q$ and all $α$. We use this classification to prove that a codeword of the Grassmann code $C(\\ell, m)$ has the second minimum weight if and only if it is indexed by an element of $\\bigwedge^{m-\\ell}V$ that can be written as the product of a decomposable $(m-\\ell-2)$-vector and an alternating $2$-vector of rank $4$. Finally, we give an enumeration of the second minimum weight codewords of the Grassmann code.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04916",
  "author_total": 2,
  "authors": [
    {
      "name": "Muskan Khaneja"
    },
    {
      "name": "Prasant Singh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c6d3cr8xkh8n1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04916",
  "fulltext_url": null,
  "id": "c6d3cr8xkh8n1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04916",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7211913667",
  "pdf_url": "https://arxiv.org/pdf/2609.04916",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c6d3cr8xkh8n1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.04916",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04916"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Minimum Schubert Codewords and Second-Minimum Grassmann Codewords",
  "title_text": "Minimum Schubert Codewords and Second-Minimum Grassmann Codewords",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/c6d3cr8xkh8n1",
  "venue": "arXiv",
  "versions": []
}