We study a tower of function fields of Artin-Schreier type over a finite field with 2 s elements. The study of the asymptotic behavior of this tower was left as an open problem by Beelen, García and Stichtenoth in 2006. We prove that this tower is asymptotically good for s even and asymptotically bad for s odd.

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A. We study the asymptotic behaviour of a family of algebraic geometry codes, which we call block-transitive, that generalizes the classes of transitive and quasi-transitive codes. We prove, by using towers of algebraic function fields, that there are sequences of codes in this family attaining the Tsfasman-Vladut-Zink bound over finite fields of square cardinality. We give the exact length of these codes as well as explicit lower bounds for their parameters.