An explicit construction of a sequence of codes attaining the Tsfasman-Vladut-Zink bound. The first steps

We present a sequence of codes attaining the Tsfasman-Vladut-Zink bound. The construction is based on the tower of Artin-Schreier extensions described by Garcia and Stichtenoth (1995). We also determine the dual codes. The first steps of the constructions are explicitly given as generator matrices.