The second largest number of points on plane curves over finite fields

被引：2
作者：
Homma, Masaaki [1 ]
Kim, Seon Jeong [2 ]
机构：
[1] Kanagawa Univ, Dept Math & Phys, Hiratsuka, Kanagawa 2591293, Japan
[2] Gyeongsang Natl Univ, Dept Math & RINS, Jinju 660701, South Korea
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2018年 / 49卷
基金：
新加坡国家研究基金会;
关键词：
Finite field; Basis of the ideal; Plane curve;
D O I：
10.1016/j.ffa.2017.09.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A basis of the ideal of the complement of a linear subspace in a projective space over a finite field is given. As an application, the second largest number of points of plane curves of degree d over the finite field of q elements is also given for d >= q + 1. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：80 / 93
页数：14
相关论文
共 50 条
[31]   On algebraic curves over a finite field with many rational points [J].
Aguglia, A ;
Korchmáros, G .
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2000, 7 (03) :333-342
[32]   Numbers of points of surfaces in the projective 3-space over finite fields [J].
Homma, Masaaki ;
Kim, Seon Jeong .
FINITE FIELDS AND THEIR APPLICATIONS, 2015, 35 :52-60
[33]   Estimating the number of roots of trinomials over finite fields [J].
Kelley, Zander ;
Owen, Sean W. .
JOURNAL OF SYMBOLIC COMPUTATION, 2017, 79 :108-118
[34]   Enumerating hyperelliptic curves over finite fields in quasilinear time [J].
Howe, Everett W. .
RESEARCH IN NUMBER THEORY, 2025, 11 (01)
[35]   On the number of rational points on an algebraic curve over a finite field [J].
Hirschfeld, JWP ;
Korchmaros, G .
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 1998, 5 (2-3) :313-340
[36]   Counting Rational Points of an Algebraic Variety over Finite Fields [J].
Hu, Shuangnian ;
Qin, Xiaoer ;
Zhao, Junyong .
RESULTS IN MATHEMATICS, 2019, 74 (01)
[37]   Numbers of points of hypersurfaces without lines over finite fields [J].
Homma, Masaaki .
TOPICS IN FINITE FIELDS, 2015, 632 :151-156
[38]   Fq-primitive points on varieties over finite fields [J].
Takshak, Soniya ;
Kapetanakis, Giorgos ;
Sharma, Rajendra Kumar .
FINITE FIELDS AND THEIR APPLICATIONS, 2025, 103
[39]   Counting Rational Points of an Algebraic Variety over Finite Fields [J].
Shuangnian Hu ;
Xiaoer Qin ;
Junyong Zhao .
Results in Mathematics, 2019, 74
[40]   ON CLASSIFICATION OF GROUPS OF POINTS ON ABELIAN VARIETIES OVER FINITE FIELDS [J].
Rybakov, Sergey .
MOSCOW MATHEMATICAL JOURNAL, 2015, 15 (04) :805-815
12345