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Cyclic triorthogonal codes in prime dimension — arXiv:2610.08012

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08012
License (as archived): CC0-1.0
Archived: 2026-10-07T12:10:26.293Z
SHA-256 of the archived text: 4ca088e58e00eb8d08c0e95924456fa6955519056f1bcd2545e508165d5fc9a4
Stable URL of this page: https://metraipolis.com/documento/dc_f8459df154cc

How to cite

Cyclic triorthogonal codes in prime dimension — arXiv:2610.08012 — arXiv (en), https://arxiv.org/abs/2610.08012 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f8459df154cc (Metraipolis archive dc_f8459df154cc, sha256 4ca088e58e00eb8d08c0e95924456fa6955519056f1bcd2545e508165d5fc9a4)

BibTeX

@misc{dcf8459df154cc,
  title = {Cyclic triorthogonal codes in prime dimension — arXiv:2610.08012},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08012},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f8459df154cc; sha256 4ca088e58e00eb8d08c0e95924456fa6955519056f1bcd2545e508165d5fc9a4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08012. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study cyclic triorthogonal codes in prime dimension $p$, on which a transversal third-level diagonal gate acts as a logical non-Clifford gate. For odd $p$, we use a definition of triorthogonality that does not require self-orthogonality. For cyclic codes of length coprime to $p$, triorthogonality reduces to a sumset condition on the spectral support, which makes exhaustive search feasible: for two natural constructions, we enumerate all maximal codes of this kind for $p=3$ up to length $121$ and $p=5,7$ up to length $96$. For qubits, we prove that a cyclic code of odd length is triply even if and only if it is classically triorthogonal, giving a complete description of triply-even cyclic codes, and we determine all such codes up to length $763$. For qudits, we find codes such as $[[19,1,3]]_3$ and $[[7,1,3]]_7$, which improve on the shortest Reed-Muller and Reed-Solomon codes in both overhead exponent and distillation threshold. The latter is the first member of an infinite family of $[[p,1,2\lfloor p/6\rfloor+1]]_p$ codes.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph) ; Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2610.08012 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:42:17.288Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).