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• W3206809046 abstract "We give a construction of quantum LDPC codes of dimension $Theta(log N)$ and distance $Theta(N/log N)$ as the code length $Ntoinfty$. Using a product of chain complexes this construction also provides a family of quantum LDPC codes of distance $Omega(N^{1-alpha/2}/log N)$ and dimension $Omega(N^alpha log N)$, where $0 le alpha < 1$. We also introduce and study a new operation called lifted product, which naturally generalizes the product operations for quantum codes and chain complexes. Moreover, as a simple byproduct of our results on quantum codes, we obtain a new result on classical codes. We show that for any fixed $R < 1$ there exists an asymptotically good family of classical quasi-cyclic LDPC codes of rate at least $R$ with, in some sense, optimal circulant size $Omega(N/log N)$ as the code length $Ntoinfty$." @default.
• W3206809046 created "2021-10-25" @default.
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• W3206809046 date "2022-01-01" @default.
• W3206809046 modified "2023-10-01" @default.
• W3206809046 title "Quantum LDPC Codes With Almost Linear Minimum Distance" @default.
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• W3206809046 doi "https://doi.org/10.1109/tit.2021.3119384" @default.
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