  We present a study to examine the sensitivity of a future $e^{-} e^{+}$
collider to the anomalous top flavour-changing neutral current (FCNC) to the
gluon. To separate signal from background a multivariate analysis is performed
on top-quark pair and background events, where one top quark is considered to
follow the dominant Standard Model (SM) decay, $t \rightarrow Wb$, and the
other top decays through FCNC, $t\rightarrow qg$, where $q$ is a $u-$ or a
$c-$quark. The analysis of fully-hadronic FCNC decay of the $t \bar{t}$ pair is
also presented. The $95\%$ confidence level limits on the top-quark anomalous
couplings are obtained for different values of the center-of-mass energies and
integrated luminosities.
