Generalized Hamming weights of trace codes

Linear codes over F_p often admit a natural representation as trace codes of codes that are defined over an extension field F_pm. In the paper, the authors obtain estimates for the weights of subcodes of such trace codes. Their main result is a far-reaching generalization of the Carlitz-Uchiyama bound for the duals of binary BCH codes. In particular, they prove sharp bounds for the generalized Hamming weights of a large class of codes, including duals of BCH codes, classical Goppa codes, Melas codes, and arbitrary cyclic codes of length n=p^m-1. The main tool is the theory of algebraic functions over finite fields, in particular the Hasse-Weil bound for the number of places of degree one