  We investigate multi-point algebraic geometric codes defined from curves
related to the generalized Hermitian curve introduced by Alp Bassa, Peter
Beelen, Arnaldo Garcia, and Henning Stichtenoth. Our main result is to find a
basis of the Riemann-Roch space of a series of divisors, which can be used to
construct multi-point codes explicitly. These codes turn out to have nice
properties similar to those of Hermitian codes, for example, they are easy to
describe, to encode and decode. It is shown that the duals are also such codes
and an explicit formula is given. In particular, this formula enables one to
calculate the parameters of these codes. Finally, we apply our results to
obtain linear codes attaining new records on the parameters. A new
record-giving $ [234,141,\geqslant 59] $-code over $ \mathbb{F}_{27} $ is
presented as one of the examples.
