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k-orthogonal, triorthogonal: asymptotically good constructions (arXiv:2609.08203) - #391

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valbert4 merged 10 commits into
errorcorrectionzoo:mainfrom
RodrigoSanJose:paper/2609.08203
Oct 13, 2026
Merged

valbert4 merged 10 commits into
errorcorrectionzoo:mainfrom
RodrigoSanJose:paper/2609.08203

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Adds results from arXiv:2609.08203 to the k-orthogonal and triorthogonal entries.

New Codes:

None.

Modified Codes:

k-orthogonal code:

  • added transversal-gate features: explicit asymptotically good binary $h$-orthogonal CSS codes where strongly transversal $R_h$, followed by a diagonal correction from level $h-1$ of the Clifford hierarchy, implements logical $R_h$ (Cor. 5.6), and $2^{h-1}$-orthogonal ones that need no correction (Cor. 6.7)

Triorthogonal code:

  • added a rate feature: asymptotically good families of binary triorthogonal codes exist

Also added myself to users/users_db.yml.

Checklist:

I remembered to:

  • Include relevant citations I could think of (with \cite{...})

  • Create links to the other referenced codes (with
    \hyperref[code:...]{...})

  • Update the relevant meta changelog fields with my user_id (see
    users/users_db.yml; add yourself in the PR if you aren't there already)

Added a note about asymptotically good families of binary triorthogonal codes. Updated changelog with new entry.
Added features for transversal gates in quantum_k-orthogonal.yml, including details on binary CSS codes and their properties.
Add note to triorthogonal codes
Updated features section with new properties for h-orthogonal binary CSS codes.
Added a rate feature to describe asymptotically good families of binary triorthogonal codes. Removed a redundant note about the same topic.
@RodrigoSanJose
RodrigoSanJose marked this pull request as ready for review October 5, 2026 20:52
@valbert4
valbert4 merged commit 6f87b0f into errorcorrectionzoo:main Oct 13, 2026
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2 participants