GENERALIZED HAMMING WEIGHTS OF TRACE CODES

Linear codes over F(p) often admit a natural representation as trace c odes of codes that are defined over an extension field F(p)m. In this paper, we obtain estimates for the weights of subcodes of such trace c odes. Our main result is a far-reaching generalization of the Carlitz- Uchiyama bound for the duals of binary BCH codes. In particular, we pr ove sharp bounds for the generalized Hamming weights of a large class of codes, including duals of BCH codes, classical Goppa codes, Melas c odes, and arbitrary cyclic codes of length n = p(m)-1. Our main tool i s the theory of algebraic functions over finite fields, in particular the Hasse-Weil bound for the number of places of degree one.