Session S29 - Theory and Applications of Coding Theory

Monday, July 19, 17:30 ~ 17:55 UTC-3

On Weierstrass gaps at several points

Guilherme Tizziotti

Universidade Federal de Uberlândia, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk we will consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado, we present a description of these elements which generalizes the approach of Homma and Kim [1] given for pairs. Through this description, we present a study of the gaps and pure gaps at several points on a certain family of curves with separated variables.

Main References

[1] M. Homma and S. J. Kim, Goppa codes with Weierstrass pairs, J. Pure Appl. Algebra 162, 2001 , 273-290.

[2] W. Tenório and G. Tizziotti, Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables, Finite Fields and Their Applications 57, 2019, 230-248.

[3] W. Tenório and G. Tizziotti, On Weierstrass gaps at several points, Bull. Brazilian Math. Society, 50, 2019, 543-559.

Joint work with Wanderson Tenório (Universidade Federal de Goiás).

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