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

Bases for Riemann-Roch spaces of one point divisors on an optimal tower of function fields