  Complex vector modes have become topical of late due to their fascinating
properties and the many applications they have found across a broad variety of
research fields. Even though such modes can be generated in a wide variety of
ways, digital holography stands out as one of the most flexible and versatile.
Along this line, Digital Micromirror Devices (DMDs) have gain popularity in
recent time due to their high refresh rates, which allows the generation of
vector modes at kHz rates. Nonetheless, most techniques are limited either by
the diversity of vector modes that can be generated or by the speed at which
they can be switched. Here we propose a technique based on the concept of
random encoding, which allows the generation of arbitrary vector beams at
speeds limited only by the refresh rate of the DMD. Our technique will be of
great relevance in research fields such as optical communications, laser
material processing and optical manipulation, amongst others.
