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Long duration gamma-ray bursts are a rare subclass of stripped-envelopecore-collapse supernovae that launch collimated relativistic outflows (jets).All gamma-ray-burst-associated supernovae are spectroscopically of Type Ic withbroad lines, but the fraction of broad-lined Type Ic supernovae harboringlow-luminosity gamma-ray-burst remains largely unconstrained. Some supernovaeshould be accompanied by off-axis $\gamma$-ray burst jets that remain invisibleinitially, but then emerge as strong radio sources (as the jets decelerate).However, this critical prediction of the jet model for gamma-ray bursts has yetto be verified observationally. Here, we present K. G. Jansky Very Large Arrayobservations of 15 broad-lined supernovae of Type Ic discovered by the PalomarTransient Factory in an untargeted manner. Most of the supernovae in our sampleexclude radio emission observationally similar to that of the radio-loud,relativistic SN\,1998bw. We constrain the fraction of 1998bw-like broad-linedType Ic supernovae to be <~ 41% (99.865% confidence). Most of the events in oursample also exclude off-axis jets similar to GRB 031203 and GRB 030329, but wecannot rule out off-axis gamma-ray-bursts expanding in a low-density windenvironment. Three supernovae in our sample are detected in the radio. PTF11qcjand PTF14dby show late-time radio emission with average ejecta speeds of~(0.3-0.4)c, on the dividing line between relativistic and "ordinary"supernovae. The speed of PTF11cmh radio ejecta is poorly constrained. Weestimate that <~ 85% (99.865% confidence) of the broad-lined Type Ic supernovaein our sample may harbor off-axis $\gamma$-ray-bursts expanding in media withdensities in the range probed by this study.

Radio observations of a sample of broad-lined type Ic supernovae discovered by PTF/iPTF: A search for relativistic explosions