\([[9m-k,k,2]]_3\) triorthogonal code[1] 

Description

Member of the \([[9m-k,k,2]]_3\) family of triorthogonal qutrit codes (for \(k\leq 3m-2\)) that admit a transversal diagonal gate in the third level of the qudit Clifford hierarchy and that are relevant for magic-state distillation.

Magic

For \(k = 3m-2\), the family yields the magic-state yield parameter \(\gamma = \log_2 (2+\frac{6}{3m-2}) \to 1\) as \(m\to\infty\) [1].

Parents

References

[1]
S. Prakash and T. Saha, “Low Overhead Qutrit Magic State Distillation”, (2024) arXiv:2403.06228
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Zoo Code ID: qutrit_small_triorthogonal

Cite as:
“\([[9m-k,k,2]]_3\) triorthogonal code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/qutrit_small_triorthogonal
BibTeX:
@incollection{eczoo_qutrit_small_triorthogonal, title={\([[9m-k,k,2]]_3\) triorthogonal code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qutrit_small_triorthogonal} }
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Permanent link:
https://errorcorrectionzoo.org/c/qutrit_small_triorthogonal

Cite as:

“\([[9m-k,k,2]]_3\) triorthogonal code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/qutrit_small_triorthogonal

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits/stabilizer/magic/qutrit_small_triorthogonal.yml.