  Core-collapse supernovae are a promising potential high-energy neutrino
source class. We test for correlation between seven years of IceCube neutrino
data and a catalog containing more than 1000 core-collapse supernovae of types
IIn and IIP and a sample of stripped-envelope supernovae. We search both for
neutrino emission from individual supernovae, and for combined emission from
the whole supernova sample through a stacking analysis. No significant spatial
or temporal correlation of neutrinos with the cataloged supernovae was found.
The overall deviation of all tested scenarios from the background expectation
yields a p-value of 93% which is fully compatible with background. The derived
upper limits on the total energy emitted in neutrinos are $1.7\times 10^{48}$
erg for stripped-envelope supernovae, $2.8\times 10^{48}$ erg for type IIP, and
$1.3\times 10^{49}$ erg for type IIn SNe, the latter disfavouring models with
optimistic assumptions for neutrino production in interacting supernovae. We
conclude that strippe-envelope supernovae and supernovae of type IIn do not
contribute more than $14.6\%$ and $33.9\%$ respectively to the diffuse neutrino
flux in the energy range of about $10^3-10^5$ GeV, assuming that the neutrino
energy spectrum follows a power-law with an index of $-2.5$. Under the same
assumption, we can only constrain the contribution of type IIP SNe to no more
than $59.9\%$. Thus core-collapse supernovae of types IIn and stripped-envelope
supernovae can both be ruled out as the dominant source of the diffuse neutrino
flux under the given assumptions.
