  We study the asymptotic behavior 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.
