{
  "abstract": "Lifted product codes are an important family of quantum low-density parity-check (QLDPC) codes, as they were the first QLDPC code family shown to be asymptotically good. Understanding the structure of their parity-check matrices $H_{\\mathsf{X}}$ and $H_{\\mathsf{Z}}$, as well as the associated Tanner graphs, is essential for analyzing their decoding behavior and error-floor performance. In this work, we show that the Tanner graphs of $H_{\\mathsf{X}}$ and $H_{\\mathsf{Z}}$ are indeed isomorphic, and investigate their graph-theoretical structure. We establish conditions ensuring the connectivity of these graphs and provide bounds on their minimal absorbing sets, providing new insight into the combinatorial structures influencing decoding performance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11987",
  "author_total": 3,
  "authors": [
    {
      "name": "Ragnar Freij-Hollanti"
    },
    {
      "name": "Kirsten D. Morris"
    },
    {
      "name": "Patricija Šapokaitė"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56watwvte94q6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11987",
  "fulltext_url": null,
  "id": "56watwvte94q6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11987",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7164336613",
  "pdf_url": "https://arxiv.org/pdf/2606.11987",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56watwvte94q6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.11987",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11987"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Graphical Analysis of Lifted Product Code Constructions",
  "title_text": "Graphical Analysis of Lifted Product Code Constructions",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/56watwvte94q6",
  "venue": "arXiv",
  "versions": []
}