Creating a weird matrix

So I'm making a documentation about Coding Theory and I'm almost over, but I'll have to create a matrix and I have no idea how to create this specific one, any help would be appreciated. A little bit of stacking can do it.

\documentclass{article}
\usepackage{stackengine}
\begin{document}
$\fboxsep=3ex\relax G=\left[ \makebox[12ex]{I_6} \addstackgap[5pt]{\vcenter{\hbox{\stackon{\fbox{S_3}}{1~1~1~1~1}}}}\, \right]$
\end{document} Some eyeballing:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$G= \begin{bmatrix} \qquad\qquad I_6 \qquad\qquad & \begin{array}{@{}|ccccc|} \multicolumn{1}{c}{1} & 1 & 1 & 1 & \multicolumn{1}{c}{1} \\ \hline &&&&\\ &&&&\\ \multicolumn{5}{|c|}{S_5\vphantom{\Bigg|}}\\ &&&&\\ &&&&\\ \hline \end{array}\, \end{bmatrix}$

\end{document} A possible solution with easybmat

\documentclass{article}
\usepackage{easybmat}

\begin{document}

$G = \left[ \begin{BMAT}(c){cc}{cc} & \begin{BMAT}{ccccc}{c} 1&1&1&1&1 \end{BMAT}\\ I_6 & \begin{BMAT}[4ex]{|c|}{|c|} S_5 \end{BMAT}\\ \end{BMAT} \right]$

\end{document} 