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Advances in Mathematics of Communications (AMC)
 

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

Pages: 67 - 72, Volume 8, Issue 1, February 2014      doi:10.3934/amc.2014.8.67

 
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Alonso SepĂșlveda - Universidade Federal de Uberlandia, Campus Santa Monica, Av. Joao Naves de Avila, 2121, Uberlandia-MG, CEP 38.408-100, Brazil (email)
Guilherme Tizziotti - Universidade Federal de Uberlandia, Campus Santa Monica, Av. Joao Naves de Avila, 2121, Uberlandia-MG, CEP 38.408-100, Brazil (email)

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.

Keywords:  Weierstrass semigroups, maximal curves, AG codes.
Mathematics Subject Classification:  Primary: 14H55; Secondary: 11G20, 14G50.

Received: November 2012;      Available Online: January 2014.

 References