(1) Faculdade de Matemática, Universidade Federal de Uberlandia, Av. J. N. Avila 2121, Uberlandia, MG, 38.408-100, Brazil;(2) Department of Mathematical Sciences, Faculty of Sciences, Yamaguchi University, Yamaguchi 753-8512, Japan
Abstract:
The concept of pure gaps of a Weierstrass semigroup at several points of an algebraic curve has been used lately to obtain
codes that have a lower bound for the minimum distance which is greater than the Goppa bound. In this work, we show that the
existence of total inflection points on a smooth plane curve determines the existence of pure gaps in certain Weierstrass
semigroups. We then apply our results to the Hermitian curve and construct codes supported on several points that compare
better to one-point codes from that same curve.