Explicit Construction of AG Codes from Generalized Hermitian Curves

We present multi-point algebraic geometric codes overstepping the Gilbert-Varshamov bound. The construction is based on the generalized Hermitian curve introduced by A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth. These codes are described in detail by constrcting a generator matrix. It turns out that these codes have nice properties similar to those of Hermitian codes. It is shown that the duals are also such codes and an explicit formula is given.