Folded quantum Reed-Solomon (FQRS) code[1] 

Description

CSS code on \(q^m\)-dimensional Galois-qudits that is constructed from folded Reed-Solomon (FRS) codes via the Galois-qudit CSS construction. This code is used to construct Singleton-bound approaching approximate quantum codes.

More technically, an \(m\)-folded quantum Reed-Solomon code is a member of the \([[n/m, R \cdot n/m, d/m]]_{q^m}\) CSS code family for any \(0<R<1\). See [1; Defn. 3.8] for an expression of the codewords. A folded quantum generalized RS (GRS) code can be defined in similar fashion from GRS codes [1; Sec. 3].

Decoding

Quantum list decodable [1].

Parent

  • Galois-qudit CSS code — Folding an quantum polynomial code on \(q\)-dimensional Galois qudits yields an FQRS code on \(q^m\)-dimensional Galois qudits.

Cousins

References

[1]
T. Bergamaschi, L. Golowich, and S. Gunn, “Approaching the Quantum Singleton Bound with Approximate Error Correction”, (2022) arXiv:2212.09935
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Zoo Code ID: galois_fqrs

Cite as:
“Folded quantum Reed-Solomon (FQRS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/galois_fqrs
BibTeX:
@incollection{eczoo_galois_fqrs, title={Folded quantum Reed-Solomon (FQRS) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/galois_fqrs} }
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Permanent link:
https://errorcorrectionzoo.org/c/galois_fqrs

Cite as:

“Folded quantum Reed-Solomon (FQRS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/galois_fqrs

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