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We examine the bright radio synchrotron counterparts of low-luminosity gamma-ray bursts (llGRBs) and relativistic supernovae (SNe) and find that they can be powered by spherical hypernova (HN) explosions. Our results imply that radio-bright HNe are driven by relativistic jets that are choked deep inside the progenitor stars or quasi-spherical magnetized winds from fast-rotating magnetars. We also consider the optical synchrotron counterparts of radio-bright HNe and show that they can bedoi:10.1088/0004-637x/805/2/164 fatcat:xps6mhhnuvhm5akj5xukjicphy