{
  "abstract": "We introduce coset lifted product (CLP) codes, a family of quantum LDPC codes that combine the protograph structure of lifted product codes with the coset action of Aydin, Tamo, and Barg \\cite{AydinTamoBarg2026}. Given a finite group $G$, a subgroup $H \\le G$ that need not be normal, a protograph $A$ over $\\mathbb F_2[G]$, and a protograph $B$ over $\\mathbb F_2[N_G(H)]$, the two protographs act on the cosets $G/H$ from the left and from the right to produce quantum CSS codes. Further, for groups of odd order, we give an explicit formula for the dimension as a sum over the irreducible representations $ρ$ of $G$ of hypergraph product dimensions. A search over $14,843$ pairs $(G,H)$ with $H$ restricted to be non-normal and $120 \\le n \\le 400$ yields certified codes that exceed the best published value of $Q=kd^2/n$ at check weights $6,7$ and $9$, i.e., we obtain $[[360,20,20]]$ at $w=6$, a $[[360,24,20]]$ code at $w=7$, and codes $[[252,16,18]]$ and $[[288,16,20]]$ at $w=9$. Our search also produce high-distance codes with parameters $[[168,10,14]], [[240,8,20]]$ at $w=6$ and $[[216,8,18]]$ at $w=7$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12782",
  "author_total": 3,
  "authors": [
    {
      "name": "Rajendra Prasad Rajpurohit"
    },
    {
      "name": "V. Lalitha"
    },
    {
      "name": "Shayan Srinivasa Garani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vpt24a1fkap7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12782",
  "fulltext_url": null,
  "id": "4vpt24a1fkap7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12782",
  "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"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221530663",
  "pdf_url": "https://arxiv.org/pdf/2610.12782",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vpt24a1fkap7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.12782",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12782"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Coset Lifted Product Codes: Constructing Quantum LDPC Codes from Non-Normal Subgroup Actions",
  "title_text": "Coset Lifted Product Codes: Constructing Quantum LDPC Codes from Non-Normal Subgroup Actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/4vpt24a1fkap7",
  "venue": "arXiv",
  "versions": []
}