\([[9,1,5]]_3\) quantum Glynn code[1]
Description
Nine-qutrit pure Hermitian code that is the smallest qutrit stabilizer code to correct two-qutrit errors.
See [2; Exam. 7] for its stabilizer generator matrix.
Protection
Smallest stabilizer code that protects against errors on any two qutrits. Detects four-qutrit errors.
Parents
Cousin
- Glynn code — Applying the Hermitian construction to the Glynn code yields a \([[10,0,6]]_3\) state [1,3]. The \([[9,1,5]]_3\) quantum Glynn code can be obtained by applying the Hermitian construction to the shortened Glynn code [1; Corr. 4] (cf. [2; Exam. 7]).
References
- [1]
- M. Grassl and M. Rotteler, “Quantum MDS codes over small fields”, 2015 IEEE International Symposium on Information Theory (ISIT) 1104 (2015) arXiv:1502.05267 DOI
- [2]
- S. Ball and R. Vilar, “The geometry of Hermitian self-orthogonal codes”, (2021) arXiv:2108.08088
- [3]
- S. Ball, “Some constructions of quantum MDS codes”, (2021) arXiv:1907.04391
Page edit log
- Victor V. Albert (2023-11-26) — most recent
Cite as:
“\([[9,1,5]]_3\) quantum Glynn code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/stab_9_1_5
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits/small/stab_9_1_5.yml.