One- and Two-Point Codes over Kummer Extensions
Abstract
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.
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