  Hypothetical particles called heavy neutral leptons (HNLs) can be produced in
large quantities in the cores of supernovae during the first seconds of the
explosion. These particles then decay, producing secondary energetic neutrinos
that can be detected by neutrino detectors. In this paper, I identify a region
of the HNL parameter space that could be tested using this method, assuming a
supernova explosion at distances from 0.2 to 10 kpc. The range of HNLs masses
$m_N \sim 160-700$ MeV and lifetimes of $\tau_N \gtrsim 0.02$ seconds can be
probed using the Hyper-Kamiokande neutrino detector. This region of the
parameter space is complementary to existing bounds from primordial
nucleosynthesis and to the expected sensitivity of the future SHiP experiment,
thus covering a gap in our current knowledge of HNLs up to masses of $m_N
\simeq 400$ MeV.
