{
  "abstract": "This paper develops a two-branch multiplicative-coset construction for regular Calderbank--Shor--Steane (CSS) quantum low-density parity-check base matrices. For a target column weight $J$ and an even row weight $L$, the method reduces regularity, CSS orthogonality, and same-type 4-cycle exclusion to explicit quotient-coset conditions over a finite field. A normalized exhaustive search for these conditions produces base matrices for several $(J,L)$ pairs, so the construction is not tied to a single degree distribution. The construction separates the finite-length design into two stages: the base matrix fixes the degree distribution and the first girth constraints, and a cyclic lift randomizes edge connections subject to exact algebraic checks. As a detailed example, we carry one $(3,10)$-regular base through the lift and decoding stages. For this example, the selected 64-fold lift gives a code whose same-type Tanner graphs have girth at least eight, and it also excludes a specified weight-16 nondegenerate logical-support orbit. Complete support enumeration excludes all nontrivial logical representatives of weight at most 16 on both sides. The resulting instance is a $[[10240,4108,\\,18\\le d\\le32]]$ CSS code. For decoding, we use joint log-domain belief propagation together with low-complexity deterministic post-processing rules for small residual syndromes, including repairs for residual patterns with two unsatisfied checks. The frame error rate (FER) measurements provide finite-length decoding data for this detailed example; at depolarizing probability $p=0.058$, the post-processing FER is $1.0\\times10^{-7}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.23894",
  "author_total": 2,
  "authors": [
    {
      "name": "Koki Okada"
    },
    {
      "name": "Kenta Kasai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3xc5earjc7v9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.23894",
  "fulltext_url": null,
  "id": "a3xc5earjc7v9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.23894",
  "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.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7162296947",
  "pdf_url": "https://arxiv.org/pdf/2605.23894",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3xc5earjc7v9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2605.23894",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.23894"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Two-Branch Finite-Field Construction for Regular CSS LDPC Bases",
  "title_text": "A Two-Branch Finite-Field Construction for Regular CSS LDPC Bases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/a3xc5earjc7v9",
  "venue": "arXiv",
  "versions": []
}