{
  "abstract": "We construct short triorthogonal codes for qudits of odd prime dimension by generalizing doubling, which combines a triorthogonal code with a code admitting a transversal phase gate, and raises the distance by up to two. This gives codes with parameters $[[28,1,4]]_3$, $[[37,1,5]]_3$, $[[72,1,6]]_3$, $[[118,1,8]]_3$, $[[33,1,5]]_5$ and $[[20,1,4]]_7$, each shorter than the cyclic, concatenated and Reed-Muller codes of the same distance, and a doubling construction of the $[[15,1,3]]_3$ code. When the columns of a generator matrix are regarded as charged points, triorthogonality becomes the vanishing of multipole moments up to octupole order, and doubling becomes a double layer of opposite charges; this picture explains why inputs with nontrivial coefficients can give shorter codes. We also show by exhaustive search that the shortest codes of distance three have length $11$ for $p=5$ and length $7$ for $p=7$. Combined with high-rate distance-two codes, the new codes reduce the cost of qutrit magic state distillation by up to an order of magnitude in regimes with high input noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29457",
  "author_total": 2,
  "authors": [
    {
      "name": "Shiroman Prakash"
    },
    {
      "name": "K. L. Ramya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6d0h4zp4j09zn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29457",
  "fulltext_url": null,
  "id": "6d0h4zp4j09zn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29457",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223212464",
  "pdf_url": "https://arxiv.org/pdf/2610.29457",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6d0h4zp4j09zn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.29457",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29457"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Short qudit triorthogonal codes from doubling",
  "title_text": "Short qudit triorthogonal codes from doubling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/6d0h4zp4j09zn",
  "venue": "arXiv",
  "versions": []
}