One- and Two-Point Codes Over Kummer Extensions
Alonso S. Castellanos, Ariane M. Masuda, Luciane Quoos · IEEE Transactions on Information Theory · 2016
We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by ym= f (x)λ, where f (x) is a separable polynomial over Fq. In addition, we compute the Weierstrass semigroup at two certain totally ramified places. We then apply our results to construct one- and two-point algebraic geometric codes with good parameters.