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Quantum twisted code[1]

Description

Hermitian stabilizer code constructed from twisted BCH codes.

Notes

Tables of quantum twisted codes are available at Yves Edel’s home page.

Cousins

  • Perfect quantum code— The \([[\frac{q^{2r}-1}{q^{2}-1},q^{n-2r},3]]_q\) family of quantum twisted codes are the only perfect Galois-qudit codes [1,2].
  • Twisted BCH code— Quantum twisted codes are quantum analogues of twisted BCH codes.

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 twisted code

References

[1]
J. Bierbrauer and Y. Edel, “Quantum twisted codes”, Journal of Combinatorial Designs 8, 174 (2000) DOI
[2]
Z. Li and L. Xing, “No More Perfect Codes: Classification of Perfect Quantum Codes”, (2009) arXiv:0907.0049
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Zoo Code ID: quantum_twisted

Cite as:
“Quantum twisted code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_twisted, arXiv:2606.11484
BibTeX:
@incollection{eczoo_quantum_twisted,
title={Quantum twisted 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_twisted}
}
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Permanent link:
https://errorcorrectionzoo.org/c/quantum_twisted

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/stabilizer/bch/quantum_twisted.yml.