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valbert4 committed Mar 30, 2024
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It is the unique code for its parameters, up to local equivalence \cite[Tab. III]{arxiv:quant-ph/9608006v5}.
Concatenations of this code with itself yield the \([[6^r,4^r,2^r]]\) level-\(r\) \textit{many-hypercube} code \cite{arxiv:2403.16054}.
Stabilizer generators are shown in \ref{figure:stab_6_4_2}.
Stabilizer generators are shown in \ref{figure:stab_6_4_2_ops}.
See \cite[Appx. B]{arxiv:2403.16054} for a set of logical Paulis.
\begin{figure}
\includegraphics{stab_6_4_2}
\caption{
Stabilizer generators of the \([[6,4,2]]\) error-detecting code.
}
\label{figure:stab_6_4_2}
\label{figure:stab_6_4_2_ops}
\end{figure}
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