Codes from curves with total inflection points
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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.
KeywordsGeometric Goppa codes Weierstrass semigroup Pure gap Total inflection point Plane curve Hermitian curve
AMS Classifications94B27 14H50 11T71 11G20
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