The result of a search for neutrino bursts from supernova explosions using the Super-Kamiokande detector is reported. Super-Kamiokande is sensitive to core-collapse supernova explosions via observation of their neutrino emissions. The expected number of events comprising such a burst is ~10^4 and the average energy of the neutrinos is in few tens of MeV range in the case of a core-collapse supernova explosion at the typical distance in our galaxy (10 kiloparsecs); this large signal means that the detection efficiency anywhere within our galaxy and well past the Magellanic Clouds is 100%. We examined a data set which was taken from May, 1996 to July, 2001 and from December, 2002 to October, 2005 corresponding to 2589.2 live days. However, there is no evidence of such a supernova explosion during the data-taking period. The 90% C.L. upper limit on the rate of core-collapse supernova explosions out to distances of 100 kiloparsecs is found to be 0.32 SN/year.
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