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Quantum plane-curve code[1]

Description

Quantum AG code constructed from plane-curve codes via the Galois-qudit Hermitian construction. Code parameters are \([[q^3,q^3+q^2-3q-2r,r+2q-q^2]]_q\), where \(r\) is an integer satisfying \(q^2 - 2 \leq r \leq q^2 + q - 3\), and where the underlying plane curve is \(y^q + y = x^{q-1}\).

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
Hermitian Galois-qudit code
Parents
Hermitian Galois-qudit code
Quantum AG codeStabilizer Hamiltonian-based QECC Quantum
Quantum plane-curve code

References

[1]
V. Nourozi, “Reinforcement Learning Enhanced Greedy Decoding for Quantum Stabilizer Codes over \(\mathbb{F}_q\)”, (2025) arXiv:2506.03397
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Zoo Code ID: quantum_plane_curve

Cite as:
“Quantum plane-curve code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_plane_curve, arXiv:2606.11484
BibTeX:
@incollection{eczoo_quantum_plane_curve,
title={Quantum plane-curve 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_plane_curve}
}
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Permanent link:
https://errorcorrectionzoo.org/c/quantum_plane_curve

Cite as:

“Quantum plane-curve code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_plane_curve, arXiv:2606.11484

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