Description
True Galois-qudit stabilizer code constructed from BCH codes via either the Hermitian construction or the Galois-qudit CSS construction. Parameters can be improved by applying Steane enlargement [8].
Notes
See Ref. [9] 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 Galois-qudit code — Galois-qudit BCH codes can be constructed via the CSS construction or the Hermitian construction.
- Subsystem Galois-qudit stabilizer code — Asymmetric quantum BCH codes have been constructed [11–13][10; Lemma 4.4], including subsystem BCH codes [14].
- Asymmetric quantum code — Asymmetric quantum BCH codes have been constructed [11–13][10; Lemma 4.4], including subsystem BCH codes [14].
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]
- Z. Ma et al., “On Non-binary Quantum BCH Codes”, Lecture Notes in Computer Science 675 (2006) DOI
- [4]
- S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, IEEE Transactions on Information Theory 53, 1183 (2007) DOI
- [5]
- R. Li et al., “Hermitian dual containing BCH codes and Construction of new quantum codes”, Quantum Information and Computation 13, 21 (2013) DOI
- [6]
- G. G. La Guardia, “Constructions of new families of nonbinary quantum codes”, Physical Review A 80, (2009) DOI
- [7]
- 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
- [8]
- G. G. La Guardia and R. Palazzo Jr., “Constructions of new families of nonbinary CSS codes”, Discrete Mathematics 310, 2935 (2010) DOI
- [9]
- A. Klappenecker, “Algebraic quantum coding theory”, Quantum Error Correction 307 (2013) DOI
- [10]
- P. K. Sarvepalli, A. Klappenecker, and M. Rötteler, “Asymmetric quantum codes: constructions, bounds and performance”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, 1645 (2009) DOI
- [11]
- L. Ioffe and M. Mézard, “Asymmetric quantum error-correcting codes”, Physical Review A 75, (2007) arXiv:quant-ph/0606107 DOI
- [12]
- S. A. Aly, “Asymmetric quantum BCH codes”, 2008 International Conference on Computer Engineering & Systems (2008) DOI
- [13]
- G. G. La Guardia, “New families of asymmetric quantum BCH codes”, Quantum Information and Computation 11, 239 (2011) DOI
- [14]
- S. A. Aly, “Asymmetric and Symmetric Subsystem BCH Codes and Beyond”, (2008) arXiv:0803.0764
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