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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 codes on Hermitian curves (see also Ref. [3]). In parameter ranges where two-point Hermitian codes improve on one-point codes, the resulting quantum codes can also have improved parameters [2].

Cousins

  • Hermitian code— Quantum Hermitian AG codes are quantum analogues of Hermitian codes.
  • Asymmetric quantum code (AQC)— One-point and two-point Hermitian codes can be used to construct asymmetric Galois-qudit CSS codes, and the two-point construction can improve on the corresponding one-point codes [2].

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.), 2026. https://errorcorrectionzoo.org/c/quantum_hermitian_ag, arXiv:2606.11484
BibTeX:
@incollection{eczoo_quantum_hermitian_ag,
title={Quantum Hermitian AG 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/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.), 2026. https://errorcorrectionzoo.org/c/quantum_hermitian_ag, arXiv:2606.11484

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