  Clusters of galaxies are the largest known gravitationally bound structures
in the Universe, with masses around $10^{15}\ M_\odot$, most of it in the form
of dark matter. The ground-based Imaging Atmospheric Cherenkov Telescope MAGIC
made a deep survey of the Perseus cluster of galaxies using almost 400 h of
data recorded between 2009 and 2017. This is the deepest observational campaign
so far on a cluster of galaxies in the very high energy range. We search for
gamma-ray signals from dark matter particles in the mass range between 200 GeV
and 200 TeV decaying into standard model pairs. We apply an analysis optimized
for the spectral and morphological features expected from dark matter decays
and find no evidence of decaying dark matter. From this, we conclude that dark
matter particles have a decay lifetime longer than $\sim10^{26}$~s in all
considered channels. Our results improve previous lower limits found by MAGIC
and represent the strongest limits on decaying dark matter particles from
ground-based gamma-ray instruments.
