One simple way is to use the array environment together the expansible brackets \left[ and \right] (note the use of {*{20}c} as suggested by @cmhughes):
\left[
\begin{array}{*{20}c}
1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0
\end{array}
\right]
The problem is the difference on the spacing for the brackets.
From the texdoc amsmath documentation:
The maximum number of columns in a matrix is determined by the counter MaxMatrixCols (normal value = 10), which you can change if necessary using
\setcounter or \addtocounter commands.
So, you can just use
\setcounter{MaxMatrixCols}{20}
\begin{equation}
\begin{bmatrix}
1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0
\end{bmatrix}
\end{equation}
{ccccccccccccc}and can use{*{20}c}– cmhughes Jan 24 '13 at 16:43\begin{array}{@{}<columns>@{}}instead, i.e.\begin{array}{@{}*{20}c@{}}. – Qrrbrbirlbel Jan 28 '13 at 02:14