\(((3,3,2))_{3}\) Three-qutrit single-deletion code

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\(((3,3,2))_{3}\) Three-qutrit single-deletion code[1]

Description

Three-qutrit PI code that is the smallest qutrit PI code to correct one deletion error.

Protection

The smallest qutrit PI code to correct one deletion error.

Cousins

\(((4,2,2))\) Four-qubit single-deletion code— The four-qubit (three-qutrit) single-deletion code is the smallest PI qubit (qutrit) code to correct one deletion error.
\([[3,1,2]]_3\) Three-qutrit code— Projecting the three-qutrit code into the PI qutrit subspace yields the three-qutrit single-deletion code [1].

Member of code lists

Primary Hierarchy

Quantum Domain

Modular-qudit Kingdom

Modular-qudit codeQECC Quantum

Parents

Modular-qudit code

Permutation-invariant (PI) codeCyclic quantum QECC Quantum

Small-distance block quantum codeQECC Quantum

\(((3,3,2))_{3}\) Three-qutrit single-deletion code

References

[1]: A. Aydin, V. V. Albert, and A. Barg, “Quantum error correction beyond \(SU(2)\): spin, bosonic, and permutation-invariant codes from convex geometry”, (2025) arXiv:2509.20545

Page edit log

Victor V. Albert (2025-10-24) — most recent

Cite as:

“\(((3,3,2))_{3}\) Three-qutrit single-deletion code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/three_qutrit_permutation_invariant

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits/small/three_qutrit_permutation_invariant.yml.