We propose to analyze the polarization and phase states of laser beams using a fixed set of non-polarizing phase elements. The experimental implementation of the proposed method is based on the use of multi-order phase-diffractive optical elements (DOEs). The presence or absence of intensity maxima (information bits) corresponding to the numbers of diffraction orders allows an identification code (a codeword) to be obtained. The resulting codeword makes it possible to uniquely determine the order of the vortex singularity and the order of the cylindrical polarization of the laser beam in various combinations based on simple relations.