  We study the extension estimates for paraboloids in d-dimensional vector
spaces over finite fields F_q with q elements. We use the connection between
L^2 based restriction estimates and L^p\to L^r extension estimates for
paraboloids. As a consequence, we improve the L^2\to L^r extension results
obtained by A. Lewko and M. Lewko in even dimensions d\ge 6 and odd dimensions
d=4\ell+3 for \ell \in \mathbb N. Our results extend the consequences for 3-D
paraboloids due to M. Lewko to higher dimensions. We also clarifies conjectures
on finite field extension problems for paraboloids.
