Description
A distance-four pure Hermitian qubit code constructed by identifying its underlying Hermitian self-orthogonal \([n,k]_4\) code with a particular projective cap in \(PG(k-1,4)\).Rate
Quantum cap codes tend to have a high rate and include a code with parameters \([[12,4,4]]\) [1].Cousin
- Projective geometry code— A quantum cap code is a distance-four pure Hermitian qubit code constructed by identifying its underlying Hermitian self-orthogonal \([n,k]_4\) code with a particular projective cap in \(PG(k-1,4)\).
Primary Hierarchy
Parents
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[n,n-2k,3]]\) Quantum cap code
References
- [1]
- 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
- [2]
- V. D. Tonchev, “Quantum codes from caps”, Discrete Mathematics 308, 6368 (2008) DOI
- [3]
- J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI
- [4]
- D. Bartoli, S. Marcugini, and F. Pambianco, “New quantum caps in PG(4,4)”, (2010) arXiv:0905.1059
- [5]
- Bierbrauer, Jürgen, D. Bartoli, S. Marcugini, and F. Pambianco. "Geometric constructions of quantum codes." Error-Correcting Codes, Finite Geometries and Cryptography 523 (2010): 149-154.
Page edit log
- Victor V. Albert (2025-06-05) — most recent
Cite as:
“\([[n,n-2k,3]]\) Quantum cap code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/quantum_cap