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Weierstrass semigroup and codes over the curve $y^q + y = x^{q^r + 1}$

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  • We compute the Weierstrass semigroup at a pair of rational points on the curve defined by the affine equation $y^q + y = x^{q^r + 1}$ over $\mathbb{F}_{q^{2r}}$, where $r$ is a positive odd integer and $q$ is a prime power. We then construct a two-point AG code on the curve whose relative parameters are better than comparable one-point AG code.
    Mathematics Subject Classification: Primary: 14H55; Secondary: 11G20, 14G50.


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