{
  "abstract": "Triorthogonal codes are a basic ingredient in magic-state distillation, as they enable transversal implementation of logical $\\mathsf{T}$ gates. As a non-Clifford operation, the $\\mathsf{T}$ gate enables universal fault-tolerant quantum computation when combined with Clifford operations. We derive an existence criterion for even-weight triorthogonal generator matrices with a target dual minimum distance. The criterion combines triorthogonality constraints with MacWilliams identities via Krawtchouk-polynomial conditions on the dual weight distribution, yielding an integer linear programming formulation for the construction problem. We find novel nontrivial triorthogonal codes (degenerate and non-degenerate) that are not necessarily constructed from triply even binary linear codes. By imposing automorphism-group constraints, the formulation also recovers the known [[49,1,5]] and [[95,1,7]] triorthogonal codes. We also evaluate the performance of the obtained high-distance triorthogonal codes over the dephasing channel using different decoding methods, showing that automorphism ensemble decoding (AED) and guessing random additive-noise decoding (GRAND) are promising options.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24519",
  "author_total": 5,
  "authors": [
    {
      "name": "Alessio Baldelli"
    },
    {
      "name": "Olai Å. Mostad"
    },
    {
      "name": "Hsuan-Yin Lin"
    },
    {
      "name": "Eirik Rosnes"
    },
    {
      "name": "Massimo Battaglioni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqwfzec5bha0s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24519",
  "fulltext_url": null,
  "id": "fqwfzec5bha0s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24519",
  "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": "W7162448113",
  "pdf_url": "https://arxiv.org/pdf/2605.24519",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqwfzec5bha0s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2605.24519",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24519"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On Constructing and Decoding Quantum Triorthogonal Codes",
  "title_text": "On Constructing and Decoding Quantum Triorthogonal Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/fqwfzec5bha0s",
  "venue": "arXiv",
  "versions": []
}