The principle of Compressed Sensing (CS) allows to find the unique sparsest solution of an under-determined system of linear equations. This is commonly used for the acquisition of a sufficiently sparse vector by a small number of measurements determined by a sensing matrix. Typically, the elements of this sensing matrix are drawn from random distributions. Calderbank et al. introduced sensing matrices based on second order Reed-Muller codes. Several reconstruction algorithms exploiting the structure of these matrices had been proposed.
The objectives of this thesis are the introduction to Reed-Muller codes and the analysis of the multiple different Reed-Muller based sensing matrix constructions with a special focus on the corresponding reconstruction algorithms.