  The IceCube Neutrino Observatory has been continuously taking data to search
for O(0.5-10) s long neutrino bursts since 2007. Even if a Galactic
core-collapse supernova is optically obscured or collapses to a black hole
instead of exploding, it will be detectable via the O(10) MeV neutrino burst
emitted during the collapse. We discuss a search for such events covering the
time between April 17, 2008 and December 31, 2019. Considering the average data
taking and analysis uptime of 91.7% after all selection cuts, this is
equivalent to 10.735 years of continuous data taking. In order to test the most
conservative neutrino production scenario, the selection cuts were optimized
for a model based on a 8.8 solar mass progenitor collapsing to an O-Ne-Mg core.
Conservative assumptions on the effects of neutrino oscillations in the
exploding star were made. The final selection cut was set to ensure that the
probability to detect such a supernova within the Milky Way exceeds 99%. No
such neutrino burst was found in the data after performing a blind analysis.
Hence, a 90% C.L. upper limit on the rate of core-collapse supernovae out to
distances of ~ 25kpc was determined to be 0.23/yr. For the more distant
Magellanic Clouds, only high neutrino luminosity supernovae will be detectable
by IceCube, unless external information on the burst time is available. We
determined a model-independent limit by parameterizing the dependence on the
neutrino luminosity and the energy spectrum.
