Bases for Riemann–Roch Spaces of One-Point Divisors on an Optimal Tower of Function Fields

For applications in algebraic geometric codes, an explicit description of bases of Riemann–Roch spaces of divisors on function fields over finite fields is needed. We give an algorithm to compute such bases for one-point divisors, and Weierstrass semigroups over an optimal tower of function fields. We also explicitly compute Weierstrass semigroups till level eight.