  In this article we analyze the reconstruction of inflation in the framework
of a non-canonical theory. In this sense, we study the viability of
reconstructing the background variables assuming a non-lineal kinetic term
given by $K(X,\phi)=X+g(\phi)X^2$, with $X$ the standard kinetic term
associated to the scalar field $\phi$ and $g(\phi)$ an arbitrary coupling
function. In order to achieve this reconstruction in the context of inflation,
we assume the slow-roll approximation together with the parametrization of the
scalar spectral index $n_s$ and the speed of sound $c_s$ as a function of the
number of $e-$folds $N$. By assuming the simplest parametrizations for
$n_s-1=-2/N$ and $c_s\propto N^{-\beta}$ with $\beta$ a constant, we find the
reconstruction of the effective potential $V(\phi)$ and the coupling function
$g(\phi)$ in terms of the scalar field. Besides, we study the reheating epoch
by considering a constant equation of state parameter, where we determine the
temperature and number of $e-$folds during the reheating epoch in terms of the
reconstructed variables and the observational parameters. In this way, the
parameter-space related to the reconstructed inflationary model are constrained
during the epochs of inflation and reheating by assuming the current
astronomical data from Planck and BICEP/Keck results.
