  A search is performed for heavy neutrinos in the decay of a $W$ boson into
two muons and a jet. The data set corresponds to an integrated luminosity of
approximately $3.0 \text{ fb}^{-1}$ of proton-proton collision data at
centre-of-mass energies of 7 and $8 \text{ TeV}$ collected with the LHCb
experiment. Both same-sign and opposite-sign muons in the final state are
considered. Data are found to be consistent with the expected background. Upper
limits on the coupling of a heavy neutrino with the Standard Model neutrino are
set at $95\%$ confidence level in the heavy-neutrino mass range from 5 to $50
\text{ GeV}/c^2$. These are of the order of $10^{-3}$ for
lepton-number-conserving decays and of the order of $10^{-4}$ for
lepton-number-violating heavy-neutrino decays.
