Generalized Weierstrass semigroups and their Poincare series

被引：2

作者：

Moyano-Fernandez, J. J. ^{[1
]}

Tenorio, W. ^{[2
]}

Torres, F. ^{[3
]}

机构：

[1] Univ Jaume 1, Inst Univ Matemat & Aplicac Castello, Campus Riu Sec, Castellon De La Plana 12071, Spain

[2] Univ Fed Uberlandia, Fac Matemat, Av JN Avila 2121, BR-38408902 Uberlandia, MG, Brazil

[3] Univ Estadual Campinas, UNICAMP, Inst Math Stat & Comp Sci IMECC, R Sergio Buarque de Holanda 651, BR-13083059 Campinas, SP, Brazil

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2019年 / 58卷

关键词：

Generalized Weicrstrass semigroups; Riemann-Roch spaces; Poincare; GOPPA CODES; POINTS; GAPS; PAIR;

D O I：

10.1016/j.ffa.2019.03.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the structure of the generalized Weierstrass semigroups at several points on a curve defined over a finite field. We present a description of these semigroups that enables us to associate them with combinatorial objects, the Poincare series and the semigroup polynomial. We show that this Poincare series determines completely the generalized Weierstrass semigroup and it is entirely determined by the semigroup polynomial. We finish the paper by describing the functional equations occurring to the Poincare series under the hypothesis of a symmetric generalized Weierstrass semigroup. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：46 / 69

页数：24

共 36 条

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