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In this paper we analyze the intersection between the norm-trace curve over F q 3 and the curves of the form y = a x 3 + b x 2 + c x + d , giving a complete characterization of the intersection between the curve and the parabolas (a=0), as well as sharp bounds for the other cases. This information is used for the determination of the weight distribution of some one-point AG codes arising from the curve. [ABSTRACT FROM AUTHOR]

We are interested in calculating the weight distribution of Hermitian codes over the finite field with q 2 elements. In this work we show that, if we can compute the partial weight distribution for about q 2 weights, then we will easily compute the whole weight distribution (which has about q 3 values). To achieve this, we actually show that the computation of a given element of the weight distribution is equivalent to a less laborious task, which is the classification of some submatrices of the parity-check matrix according to their rank. [ABSTRACT FROM AUTHOR]