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
- Plane-curve code
- Small-distance block quantum code— The quantum plane-curve code for the Hermitian curve \(y^3 + y = x^4\) is a \([[27,13,4]]_3\) qutrit code.
Primary Hierarchy
Parents
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
Page edit log
- Victor V. Albert (2025-06-05) — most recent
Cite as:
“Quantum plane-curve code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/quantum_plane_curve