  Reed-Muller codes belong to the family of affine-invariant codes. As such
codes they have a defining set that determines them uniquely, and they are
extensions of cyclic group codes. In this paper we identify those cyclic codes
with multidimensional abelian codes and we use the techniques introduced in
\cite{BS} to construct information sets for them from their defining set. For
first and second order Reed-Muller codes, we describe a direct method to
construct information sets in terms of their basic parameters.
