Weierstrass semigroups at every point of the Suzuki curve

Published on Jan 1, 2021in Acta Arithmetica0.608
· DOI :10.4064/AA181203-24-2
Daniele Bartoli16
Estimated H-index: 16
,
Maria Montanucci10
Estimated H-index: 10
,
Giovanni Zini10
Estimated H-index: 10
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Abstract
In this article we explicitly determine the structure of the Weierstrass semigroups H(P)for any point Pof the Suzuki curve \mathcal{S}_q As the point Pvaries, exactly two possibilities arise for H(P) one for the \mathbb{F}_qrational points (already known in the literature), and one for all remaining points. For this last case a minimal set of generators of H(P)is also provided. As an application, we construct dual one-point codes from an \mathbb{F}_{q^4}\setminus\fqpoint whose parameters are better in some cases than the ones constructed in a similar way from an \fqrational point.
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#1Peter Beelen (DTU: Technical University of Denmark)H-Index: 16
#2Leonardo Landi (DTU: Technical University of Denmark)H-Index: 1
Last. Maria Montanucci (DTU: Technical University of Denmark)H-Index: 10
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Abstract In [14] , D. Skabelund constructed a maximal curve over F q 4 as a cyclic cover of the Suzuki curve. In this paper we explicitly determine the structure of the Weierstrass semigroup at any point P of the Skabelund curve. We show that its Weierstrass points are precisely the F q 4 -rational points. Also we show that among the Weierstrass points, two types of Weierstrass semigroup occur: one for the F q -rational points, one for the remaining F q 4 -rational points. For each of these two ...
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