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
- Folded RS (FRS) code
- Generalized RS (GRS) code — A folded quantum generalized RS (GRS) code can be constructed in similar fashion from GRS codes as FQRS codes are constructed from FRS codes [1; Sec. 3].
- Singleton-bound approaching AQECC — Singleton-bound approaching AQECCs utilize FQRS codes.
- Galois-qudit RS code — A FQRS code with no extra grouping (\(m=1\)) reduces to a Galois-qudit RS code that is CSS.
References
- [1]
- T. Bergamaschi, L. Golowich, and S. Gunn, “Approaching the Quantum Singleton Bound with Approximate Error Correction”, (2022) arXiv:2212.09935
Page edit log
- Victor V. Albert (2023-01-08) — most recent
- Sam Gunn (2022-01-08)
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