Theory of algebraic curves with application toward the coding theory

本研究的最初目的是研究具有特殊性质的代数曲线，并将其成果应用于编码理论。我们列出了项目负责人主要关注的我们收获的简短摘要。在研究经典的Castelnuovo理论时，我们提出了特殊因子的新的不变量“特殊性的阶”，并给出了在不变量意义下的极值曲线的分类.我们考虑了两点AG码，并证实了它的参数在一定情况下优于单点码。此外，我们开始研究Hermitian曲线上的所有两点编码，但仍在进行中.我们于2002年1月28日至31日在山口大学组织了国际会议“曲线02”，然后编辑了会议录。

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.