braces over matrix

Here's one way... [EDITED, added \mkern to address barbara's concern; REEDITED to make use of \overbrace superscript]

\documentclass{article}
\usepackage{amsmath}
\usepackage{stackengine}
\begin{document}
\def\tmp{%
  \begin{pmatrix}
  1 & 1 & 0 & .& . & . & 0 & 1  \\
  0 & 0 & 1 & .& . & . & 1 & 0 \\
 .\\
 .\\
 .\\
  0 & 1 & 1 & . & . & . & 1 & 1
 \end{pmatrix}
}%
\[
\stackMath\def\stackalignment{r}%
  \stackon%
    {\mathrm{10~rows}\left\{\tmp\right.}%
    {\overbrace{\phantom{\smash{\tmp\mkern -36mu}}}^{\mathrm{\textstyle 12~columns}}\mkern 20mu}%
\]
\end{document}

The following requires some \nulldelimiterspace corrections, but only uses amsmath:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\def\matriximg{%
  \begin{matrix}
    1 & 1 & 0 & \cdot & \cdot & \cdot & 0 & 1 \\
    0 & 0 & 1 & \cdot & \cdot & \cdot & 1 & 0 \\
    \cdot                                     \\
    \cdot                                     \\
    \cdot                                     \\
    0 & 1 & 1 & \cdot & \cdot & \cdot & 1 & 1
   \end{matrix}
}%
\[
  \text{\scriptsize 10~rows}\left\{\left(\vphantom{\matriximg}\right.\right.\kern-2\nulldelimiterspace
  \overbrace{\matriximg}^{\text{12 columns}}\kern-\nulldelimiterspace\left.\vphantom{\matriximg}\right)
\]

\end{document}

For raising the \overbrace slightly, you could use

\vphantom{\raisebox{.25\baselineskip}{$\matriximg$}}\matriximg