Multimode fibers have been extensively used in short-range communication systems and optical imaging. More recently, they have been considered for optical computing by exploiting the complex spatial and spatio-temporal transformation at the fiber end. Mimicking the dendrites of real neurons, we consider here the spatial modes that propagate with different group velocities along the fiber as different dendritic branches. The multimode fiber plays the role of an optical dendritic unit and the signals obtained from the different dendritic branches are temporally mixed and used for spatio-temporal information processing. We numerically demonstrate the use of a few-mode, step-index fiber as a linear computing element in an ultra-fast spatio-temporal coincidence detector that operates at 40 Gb/s data encoding rate. We evaluate this detector as a linear classifier in header recognition and bit counting tasks.