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

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3 Author(s)
Noseda, F. ; Inst. de Mat., Univ. Fed. do Rio de Janeiro, Rio de Janeiro, Brazil ; Oliveira, G. ; Quoos, L.

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.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 5 )