Quantum cyclic code[1]

Description

A code \(C\) constructed in a physical space consisting of a tensor product of \(n\) subsystems (e.g., qubits) is cyclic if a cyclic permutation of the subsystems leaves the code subspace invariant.

Protection

Cyclic symmetry guarantees that if a single subsystem is protected against some noise, then all other subsystems are also.

Decoding

Adapted from the Berlekamp decoding algorithm for classical BCH codes [1].

Notes

Many examples have been found by computer algebra programs. Ref. [1] give examples of \([[17,1,7]]\) and \([[17,9,3]]\) quantum cyclic codes.

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Zoo code information

Internal code ID: quantum_cyclic

Your contribution is welcome!

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Zoo Code ID: quantum_cyclic

Cite as:
“Quantum cyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_cyclic
BibTeX:
@incollection{eczoo_quantum_cyclic, title={Quantum cyclic code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_cyclic} }
Permanent link:
https://errorcorrectionzoo.org/c/quantum_cyclic

References

[1]
Sagarmoy Dutta and Piyush P Kurur, “Quantum Cyclic Code”. 1007.1697

Cite as:

“Quantum cyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_cyclic

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/quantum_cyclic.yml.