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In this article we describe how to find the parameters of subfield subcodesof 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 determinethe dimension of the subfield subcodes or the dimension of the trace code. Wealso find a BCH--like bound from the minimum distance of the originalsupercode.

On Parameters of Subfield Subcodes of Extended Norm-Trace Codes