  Neutral-current production of $K^{+}$ by atmospheric neutrinos is a
background in searches for the proton decay $p \rightarrow K^{+} \bar{\nu}$.
Reactions such as $\nu p \rightarrow \nu K^{+} \Lambda$ are indistinguishable
from proton decays when the decay products of the $\Lambda$ are below detection
threshold. Events with $K^{+}$ are identified in MINERvA by reconstructing the
timing signature of a $K^{+}$ decay at rest. A sample of 201 neutrino-induced
neutral-current $K^{+}$ events is used to measure differential cross sections
with respect to the $K^{+}$ kinetic energy, and the non-$K^{+}$ hadronic
visible energy. An excess of events at low hadronic visible energy is observed
relative to the prediction of the NEUT event generator. Good agreement is
observed with the cross section prediction of the GENIE generator. A search for
photons from $\pi^{0}$ decay, which would veto a neutral-current $K^{+}$ event
in a proton decay search, is performed, and a 2$\sigma$ deficit of detached
photons is observed relative to the GENIE prediction.
