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valbert4 committed Oct 16, 2023
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description: |
A quasi-cyclic Galois-qudit CSS code constructed using a generalized version of the bicycle ansatz \cite{arXiv:quant-ph/0304161} from a pair of equivalent index-two quasi-cyclic linear codes.
Various instances of qubit GB codes are constructed in \cite{arXiv:2203.17216} (only codes with \(k=2\)) and in \cite{arXiv:2306.16400}.
The stabilizer generator matrix of a \([[ n=2\ell,k,d]]\) denoted GB\((a,b)\) code over \(GF(q)\), constructed from polynomials \(a(x)\) and \(b(x)\), can be refined to the form
\begin{align}
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decoders:
- 'BP-OSD decoder \cite{arXiv:1904.02703}.'

realizations:
Many instances of binary (qubit-based) GB codes are constructed in \cite{arXiv:2203.17216} (only codes with \(k=2\)) and in \cite{arXiv:2306.16400}.

relations:
parents:
- code_id: galois_css
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