Codes from curves with total inflection points

被引：8
作者：
Carvalho, Cicero
Kato, Takao
机构：
[1] Univ Fed Uberlandia, Fac Matemat, BR-38408100 Uberlandia, MG, Brazil
[2] Yamaguchi Univ, Dept Math Sci, Fac Sci, Yamaguchi 7538512, Japan
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2007年 / 45卷 / 03期
关键词：
geometric goppa codes; Weierstrass semigroup; pure gap; total inflection point; plane curve; Hermitian curve;
D O I：
10.1007/s10623-007-9129-7
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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.
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页码：359 / 364
页数：6
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