Trace description of q-ary linear codes

J. Wolfmann (see A.A.E.C.C., vol.2, p.119, 1991) gives a description of projective binary linear codes by means of a polynomial. The purpose of our work is first to generalize such a description to q-ary codes. Then the main difficulty is to evaluate the weights of these codes and it is not possible to follow the same method as in the binary case. We consider Artin-Schreier curves and we give a bound on weights. Some normalization are also investigated.<>