Description
True Galois-qudit stabilizer code constructed from BCH codes via either the Hermitian construction or the Galois-qudit CSS construction.
Notes
See Ref. [7] for an overview of quantum BCH codes.
Parent
- True Galois-qudit stabilizer code — Galois-qudit BCH codes can be constructed via the CSS construction or the Hermitian construction.
Child
- Qubit BCH code — Galois-qudit BCH codes for \(q=2\) reduce to qubit BCH codes.
Cousins
- Bose–Chaudhuri–Hocquenghem (BCH) code
- Galois-qudit CSS code — Galois-qudit BCH codes can be constructed via the CSS construction or the Hermitian construction.
- Hermitian-construction code — Galois-qudit BCH codes can be constructed via the CSS construction or the Hermitian construction.
References
- [1]
- S. Aly, A. Klappenecker, and P. K. Sarvepalli, “Primitive Quantum BCH Codes over Finite Fields”, (2006) arXiv:quant-ph/0501126
- [2]
- S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, (2006) arXiv:quant-ph/0604102
- [3]
- S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, IEEE Transactions on Information Theory 53, 1183 (2007) DOI
- [4]
- R. Li et al., “Hermitian dual containing BCH codes and Construction of new quantum codes”, Quantum Information and Computation 13, 21 (2013) DOI
- [5]
- G. G. La Guardia, “Constructions of new families of nonbinary quantum codes”, Physical Review A 80, (2009) DOI
- [6]
- X. Zhao et al., “Hermitian dual-containing constacyclic BCH codes and related quantum codes of length \(\frac{q^{2m}-1}{q+1}\)”, (2020) arXiv:2007.13309
- [7]
- A. Klappenecker, “Algebraic quantum coding theory”, Quantum Error Correction 307 (2013) DOI
Page edit log
- Victor V. Albert (2022-07-22) — most recent
Cite as:
“Galois-qudit BCH code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/galois_bch