Weierstrass Semigroups From a Tower of Function Fields Attaining the Drinfeld-Vladut Bound

11/07/2019

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by   Shudi Yang, et al.

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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 investigate the third function field F^(3) in a tower of Artin-Schreier extensions described by Garcia and Stichtenoth reaching the Drinfeld-Vlăduţ bound. We construct bases for the related Riemann-Roch spaces on F^(3) and present some basic properties of divisors on a line. From the bases, we explicitly calculate the Weierstrass semigroups and pure gaps at several places on F^(3). All of these results can be viewed as a generalization of the previous work done by Voss and Høholdt (1997).