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Subsystem Galois-qudit CSS code[1,2]

Alternative Names: Euclidean construction subsystem code.

Description

Galois-qudit subsystem stabilizer code which admits a set of gauge-group generators which consist of either all-\(Z\) or all-\(X\) Galois-qudit Pauli strings.

These codes can be constructed from classical codes via a subsystem generalization of the CSS construction or the Hermitian construction [1,3].

Cousin

  • Galois-qudit CSS code— Subsystem Galois-qudit CSS codes reduce to (subspace) Galois-qudit CSS codes when there is no gauge subsystem.

Member of code lists

Primary Hierarchy

Quantum Domain
Galois-qudit Kingdom
Subsystem Galois-qudit codeSubsystem QECC Quantum
Subsystem Galois-qudit stabilizer codeSubsystem QECC Quantum
Parents
Subsystem Galois-qudit stabilizer code
Subsystem CSS codeSubsystem QECC Quantum
Subsystem Galois-qudit CSS code
Children
Subsystem qubit CSS code
Subsystem Galois-qudit CSS codes reduce to subsystem qubit CSS codes for \(q=2\).

References

[1]
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “Subsystem Codes”, (2006) arXiv:quant-ph/0610153
[2]
S. A. Aly and A. Klappenecker, “Constructions of Subsystem Codes over Finite Fields”, (2008) arXiv:0811.1570
[3]
A. Klappenecker and P. K. Sarvepalli, “Clifford Code Constructions of Operator Quantum Error Correcting Codes”, (2006) arXiv:quant-ph/0604161
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Zoo Code ID: galois_subsystem_css

Cite as:
“Subsystem Galois-qudit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/galois_subsystem_css, arXiv:2606.11484
BibTeX:
@incollection{eczoo_galois_subsystem_css,
title={Subsystem Galois-qudit CSS code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/galois_subsystem_css}
}
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Permanent link:
https://errorcorrectionzoo.org/c/galois_subsystem_css

Cite as:

“Subsystem Galois-qudit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/galois_subsystem_css, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/subsystem/galois_subsystem_css.yml.