The association of gamma-ray bursts (GRBs) and core-collapse supernovae (SNe) of Type Ib and Ic was motivated by the detection of SN 1998bw in the error box of GRB 980425 and the now-secure identification of a SN 1998bw-like event in the cosmological GRB 030329. The bright radio emission from SN 1998bw indicated that it possessed some of the unique attributes expected of GRBs, namely a large reservoir of energy in (mildly) relativistic ejecta and variable energy input. The two popular scenarios for the origin of SN 1998bw are a typical cosmological burst observed off-axis or a member of a new distinct class of supernova explosions (gSNe). In the former, about 0.5% of local Type Ib/c SNe are expected to be similar to SN1998bw; for the latter no such constraint exists. Motivated thus, we began a systematic program of radio observations of most reported Type Ib/c SNe accessible to the Very Large Array. Of the 33 SNe observed from late 1999 to the end of 2002 at most one is as bright as SN 1998bw. From this we conclude that the incidence of such events is <3%. Furthermore, analysis of the radio emission indicates that none of the observed SNe exhibit clear engine signatures. Finally, a comparison of the SN radio emission to that of GRB afterglows indicates that none of the SNe could have resulted from a typical GRB, independent of the initial jet orientation. Thus, while the nature of SN 1998bw remains an open question, there appears to be a clear dichotomy between the majority of hydrodynamic and engine-driven explosions.

18 pages, 6 figures, 3 tables