Description
Nine-qubit pure Hermitian qubit code constructed from the almost MDS \([9,3,6]_4\) Hermitian self-orthogonal code. The code can be constructed from the elliptic quadric in \(PG(5, 2)\) [2]. It is the only pure Hermitian code with its parameters [3; ID 170235] and is the highest-distance qubit stabilizer code for its \(n\) and \(k\).Cousin
- Projective geometry code— The \([[9,3,3]]\) quadric code can be constructed from the elliptic quadric in \(PG(5, 2)\) [2].
Primary Hierarchy
Parents
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[9,3,3]]\) Quadric code
References
- [1]
- I. Bouyukliev and P. R. J. Östergard, “Classification of Self-Orthogonal Codes over \boldmath\(\F_3\) and \boldmath\(\F_4\)”, SIAM Journal on Discrete Mathematics 19, 363 (2005) DOI
- [2]
- J. Bierbrauer, G. Faina, M. Giulietti, S. Marcugini, and F. Pambianco, “The geometry of quantum codes”, Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial 6, 53 (2008) DOI
- [3]
- A. Cross and D. Vandeth, “Small Binary Stabilizer Subsystem Codes”, (2025) arXiv:2501.17447
Page edit log
- Victor V. Albert (2025-06-05) — most recent
Cite as:
“\([[9,3,3]]\) Quadric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/stab_9_3_3