Theory of algebraic curves with application toward the coding theory

代数曲线理论及其在编码理论中的应用

• 批准号: 13640048
• 负责人: HOMMA Masaaki
• 金额: $ 1.34万
• 依托单位: Kanagawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640048/
• 关键词: Algebraic Curve; Special Divisor; Weierstrass pair; AG Code; Error correcting Code; Hermitian Curve; 誤り訂正符号; 代数幾何符号; 特殊線形系; Castelnuovo's bound; 国際研究者交流; ブラジル:韓国

The initial purpose of this research was to study algebraic curves with distinctive properties and apply its fruit to coding theory. We list the very short summaries of our harvests that the chief of the project was mainly concerned with.1. We proposed the new invariant "the order of speciality" of a special divisor while we were studing the classical theory of Castelnuovo, and gave a classification of the curves that are extremal in the sense of the invariant.2. We considered the two points AG-code and confirmed that its parameters are better than those of a one point code in a certain situation. Moreover we started to investigate all two points codes on a Hermitian curve, however it is still in progress.3. We organized the international conference "Curve 02" at Yamaguchi university January 28 - 31, 2002, and then edited the proceedings.

这项研究的最初目的是研究具有独特特性的代数曲线，并将其果实应用于编码理论。我们列出了该项目负责人主要关注的收成的简短摘要。1。我们提出了新的不变的特殊除法者的“专业秩序”，而我们正在研究Castelnuovo的古典理论，并将其分类从不变的意义上进行了极大的曲线。2。我们考虑了两个点AG代码，并确认其参数比某种情况下的一个点代码的参数更好。此外，我们开始在Hermitian曲线上调查所有两个点代码，但是仍在进行中。3。我们在2002年1月28日至31日在山口大学组织了国际会议“曲线02”，然后编辑了诉讼程序。

项目成果

T.Kato.: "Martens' dimension theorem for curves of odd gonality"J. Korean Mats Soc.. 39. 665-680 (2002)

T.Kato.：“奇角性曲线的马滕斯维数定理”J.

Kim, S.J., Komeda, J.: "Weierstrass semigroups of a pair of points whose first non-gaps are three"Geom. Dedicata. 93. 113-119 (2002)

Kim, S.J., Komeda, J.：“一对点的 Weierstrass 半群，其第一个非间隙是 3”Geom。

T.Kato., and Miyako Yamada.: "Projective systems whose supports consist of the union of three linear subspaces"Bull. Korean Math. Soc.. 38. 689-699 (2001)

T.Kato. 和 Miyako Yamada.：“其支撑由三个线性子空间的并集组成的投影系统”Bull。

J.Komeda.: "Numerical semigroups of toric type of higher dimension"RIMS Kokyuroku. 1268. 77-80 (2002)

J.Komeda.：“高维环面型数值半群”RIMS Kokyuroku。

T.Kato.: "A characterization of the Fermat curve"Nonlinear Analysis. 47. 5479-5489 (2001)

T.Kato.：“费马曲线的表征”非线性分析。