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Quantum Hermitian AG code[1,2]

Description

Quantum AG code constructed from Hermitian AG codes via the Galois-qudit Hermitian construction or the Galois-qudit CSS construction. The underlying classical codes can be constructed from one-point [1] or two-point [2] Hermitian curves (see also Ref. [3]).

Cousins

Member of code lists

Primary Hierarchy

Quantum Domain
Galois-qudit Kingdom
Galois-qudit codeQECC Quantum
Galois-qudit USt code
Galois-qudit stabilizer codeStabilizer Hamiltonian-based QECC Quantum
True Galois-qudit stabilizer code
Quantum AG code
Parents
Quantum AG code
Quantum Hermitian AG code

References

[1]
P. K. Sarvepalli and A. Klappenecker, “Nonbinary Quantum Codes from Hermitian Curves”, Lecture Notes in Computer Science 136 (2006) DOI
[2]
M. F. Ezerman and R. Kirov, “Nonbinary Quantum Codes from Two-Point Divisors on Hermitian Curves”, (2011) arXiv:1102.3605
[3]
L. Sok, “New families of quantum stabilizer codes from Hermitian self-orthogonal algebraic geometry codes”, (2021) arXiv:2110.00769
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Zoo Code ID: quantum_hermitian_ag

Cite as:
“Quantum Hermitian AG code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/quantum_hermitian_ag
BibTeX:
@incollection{eczoo_quantum_hermitian_ag, title={Quantum Hermitian AG code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_hermitian_ag} }
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Permanent link:
https://errorcorrectionzoo.org/c/quantum_hermitian_ag

Cite as:

“Quantum Hermitian AG code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/quantum_hermitian_ag

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/stabilizer/evaluation/ag/quantum_hermitian_ag.yml.