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

Alonso Sepúlveda; Guilherme Tizziotti

doi:10.3934/amc.2014.8.67

Article Contents

2014, Volume 8, Issue 1: 67-72. Doi: 10.3934/amc.2014.8.67

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

Alonso Sepúlveda^1, and
Guilherme Tizziotti^1,

1.
Universidade Federal de Uberlandia, Campus Santa Monica, Av. Joao Naves de Avila, 2121, Uberlandia-MG, CEP 38.408-100

Received: November 2012

Published: February 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 14H55; Secondary: 11G20, 14G50.

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