{
  "abstract": "The random $k$-XORSAT matrix is an $m\\times n$ random matrix $\\mathbf A$ over $\\mathbb F_2$ that represents a random instance of the $k$-XORSAT problem. Each row of $\\mathbf A$ contains precisely $k\\geq3$ non-zero entries in random positions. The rows are drawn independently. The matrix $\\mathbf A$ is known to have full row rank for $m/n$ below the random $k$-XORSAT satisfiability threshold, which is known explicitly [Dubois, Mandler~2002; Pittel, Sorkin~2016]. Motivated by a problem from quantum game theory and refining a result of Cooper, Frieze and Pegden (2019), we determine the limiting distribution of the rank of $\\mathbf A$ beyond the satisfiability threshold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26300",
  "author_total": 2,
  "authors": [
    {
      "name": "Amin Coja-Oghlan"
    },
    {
      "name": "Maurice Rolvien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mx9yex7rm2se.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26300",
  "fulltext_url": null,
  "id": "9mx9yex7rm2se",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26300",
  "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.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1705|Constraint Satisfaction and Optimization"
    ]
  ],
  "openalex": "W7223051752",
  "pdf_url": "https://arxiv.org/pdf/2610.26300",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mx9yex7rm2se.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26300",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26300"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The rank of the random $k$-XORSAT matrix beyond satisfiability",
  "title_text": "The rank of the random k-XORSAT matrix beyond satisfiability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/9mx9yex7rm2se",
  "venue": "arXiv",
  "versions": []
}