On Parameters of Subfield Subcodes of Extended Norm-Trace Codes

Abstract

In this article we describe how to find the parameters of subfield subcodes of extended Norm--Trace codes. With a Gröbner 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.