Distance-balanced code[1][2]

Description

CSS stabilizer code constructed from a CSS code and a classical code using a distance-balancing procedure based on a generalized homological product. The initial code is said to be unbalanced, i.e., tailored to noise biased toward either bit- or phase-flip errors, and the procedure can result in a code that is treats both types of errors on a more equal footing. The original distance-balancing procedure [1], later generalized in Ref. [2], can yield QLDPC codes; see Thm. 1 in Ref. [1].

Parents

Cousins

Zoo code information

Internal code ID: distance_balanced

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Zoo Code ID: distance_balanced

Cite as:
“Distance-balanced code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/distance_balanced
BibTeX:
@incollection{eczoo_distance_balanced, title={Distance-balanced code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/distance_balanced} }
Permanent link:
https://errorcorrectionzoo.org/c/distance_balanced

References

[1]
M. B. Hastings, “Weight Reduction for Quantum Codes”. 1611.03790
[2]
Shai Evra, Tali Kaufman, and Gilles Zémor, “Decodable quantum LDPC codes beyond the $\sqrt{n}$ distance barrier using high dimensional expanders”. 2004.07935
[3]
N. P. Breuckmann and J. N. Eberhardt, “Balanced Product Quantum Codes”, IEEE Transactions on Information Theory 67, 6653 (2021). DOI; 2012.09271

Cite as:

“Distance-balanced code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/distance_balanced

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/qldpc/distance_balanced.yml.