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Weierstrass Semigroup and Pure Gaps at Several Points on the GK Curve

Weierstrass Semigroup and Pure Gaps at Several Points on the GK Curve We determine the Weierstrass semigroup $$H(P_{\infty }, P_{1}, \ldots , P_{m})$$ H ( P ∞ , P 1 , … , P m ) at several points on the GK curve. In addition, we present conditions to find pure gaps on the set of gaps $$G(P_{\infty }, P_{1}, \ldots , P_{m})$$ G ( P ∞ , P 1 , … , P m ) . Finally, we apply the results to obtain AG codes with good relative parameters. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Weierstrass Semigroup and Pure Gaps at Several Points on the GK Curve

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-017-0059-3
Publisher site
See Article on Publisher Site

Abstract

We determine the Weierstrass semigroup $$H(P_{\infty }, P_{1}, \ldots , P_{m})$$ H ( P ∞ , P 1 , … , P m ) at several points on the GK curve. In addition, we present conditions to find pure gaps on the set of gaps $$G(P_{\infty }, P_{1}, \ldots , P_{m})$$ G ( P ∞ , P 1 , … , P m ) . Finally, we apply the results to obtain AG codes with good relative parameters.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Nov 25, 2017

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