Description
Six-qudit MDS error-detecting code defined for Galois-qudit dimension \(q=3\) [1], \(q=2^2\) [3], and \(q \geq 5\) [1,2]. This code cannot exist for qubits (\(q=2\)).
Encoding
Three different encoding circuits for \(q=3\) [4].
Parents
- True Galois-qudit stabilizer code — The code is a non-CSS stabilizer code in general [3].
- Quantum maximum-distance-separable (MDS) code
- Small-distance block quantum code
Cousin
- Graph quantum code — The \([[6,2,3]]_{q}\) code family contains examples of graph quantum codes [1].
References
- [1]
- Keqin Feng, “Quantum codes [[6, 2, 3]]/sub p/ and [[7, 3, 3]]/sub p/ (p ≥ 3) exist”, IEEE Transactions on Information Theory 48, 2384 (2002) DOI
- [2]
- A. Ketkar et al., “Nonbinary stabilizer codes over finite fields”, (2005) arXiv:quant-ph/0508070
- [3]
- Z. Wang et al., “Quantum error-correcting codes over mixed alphabets”, Physical Review A 88, (2013) arXiv:1205.4253 DOI
- [4]
- M. Grassl, “Variations on Encoding Circuits for Stabilizer Quantum Codes”, Lecture Notes in Computer Science 142 (2011) DOI
Page edit log
- Victor V. Albert (2024-03-01) — most recent
Cite as:
“\([[6,2,3]]_{q}\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/galois_6_2_3