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.

翻译：Reed-Muller码属于仿射不变码族。作为此类码，它们具有唯一确定自身的定义集，且是循环群码的扩展。本文将此类循环码与多维阿贝尔码进行对应，并利用文献\cite{BS}中的方法从其定义集构造信息集。针对第一类和第二类Reed-Muller码，我们提出一种基于其基本参数直接构造信息集的方法。