Let C $\subseteq$ $ \mathbb{Z}_2^5$be a linear code with generator matrix $$G=\begin{bmatrix}1 & 0 & 0 & 1 & 1\\ 0 & 1 & 0 & 1 & 1\\0 & 0 & 1 & 0 & 1\end{bmatrix}$$.
Show that C is not 1-error correcting by finding a received word that cannot be correctly decoded using Slepian decoding.
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