  In this article we describe how to find the parameters of subfield subcodes
of extended Norm--Trace codes. With a Gr\"obner basis of the ideal of the
$\mathbb{F}_{q^r}$ rational points of the Norm--Trace curve one can determine
the dimension of the subfield subcodes or the dimension of the trace code. We
also find a BCH--like bound from the minimum distance of the original
supercode.
