Weierstrass semigroups in an asymptotically good tower of function fields (Q1273214)

\textit{A. Garcia} and \textit{H. Stichtenoth} [J. Number Theory 61, No. 2, 248-273 (1996; Zbl 0893.11047)] gave an explicit example of an asymptotically good tower of function fields over a finite field \({\mathbb F}_{q^2}\) that achieves the Drinfeld-Vladut bound. (This example is somewhat easier to handle than their first such example in [Invent. Math. 121, 211-222 (1995; Zbl 0822.11078)].) In this tower, the first function field is the rational function field \({\mathbb F}_{q^2}(x_1)\), and the function \(x_1\) has a unique pole \(P^{(m)}\) in each function field \(T_m\) in the tower. The authors give an explicit description of the Weierstrass semigroup of \(P^{(m)}\) in \(T_m\). (However, they do not give bases for the Riemann-Roch spaces \(L(rP^{(m)})\). If one knew such bases, one could give an explicit family of codes that attains the Tsfasman-Vladut-Zink bound).