\([[6,2,3]]_{q}\) code[1,2] 

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

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
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Zoo Code ID: galois_6_2_3

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
BibTeX:
@incollection{eczoo_galois_6_2_3, title={\([[6,2,3]]_{q}\) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/galois_6_2_3} }
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https://errorcorrectionzoo.org/c/galois_6_2_3

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/small/galois_6_2_3.yml.