Axions represent a class of particles that emerge in theoretical models explaining several mysteries of high-energy particle physics and cosmology. They explain the absence of CP violation in the strong interaction, provide dark matter candidates, and can be responsible for inflation and structure formation in the early universe. Several searches for axions and axion-like particles have constrained the parameter space over the last decades, however, no hints of axions have been found. The mass range of 1-1000 × 10^-6 eV remains highly attractive and well motivated region for dark matter axions. In the white paper below we present a description of a new experiment based on the concept of a dielectric haloscope for the search for dark matter axions in the mass range 40-400 × 10^-6eV. The experiment, called MADMAX, will consist of several parallel dielectric layers, whose separations can be adjusted and are placed in a strong magnetic field. This would lead to the emission of axion induced electromagnetic waves in the 10-100 GHz domain, with the frequency given by the axion mass.