In this paper, we summarize the foundations of Algebraic function fields, algebraic curves over finite fields and algebraic geometry codes, then we focus on the dimensions of codes on the quotient of the hermitian curves, by using the theory of weierstrass semigroup and the idea of Ho.
我们在系统地总结了代数函数域,有限域上的代数曲线和代数几何码的基本知识的基础上,利用Weierstrass子半群理论,使用Homma和Kim的方法,讨论了Hermite曲线商域上码的维数问题,得到的主要结果如下:1。
g′) denotes the genus of the algebraic function field K(resp.
首先计算出了代数闭域上的有理函数域的位的次数,然后利用代数函数域的Kummer扩张的亏格关系,给出了具体计算形如C∶yn=(x-a1)n1(x-a2)n2…(x-as)ns的曲线的亏格公式。
For general real quadratic algebraic function field K, a theorem on the fundamental unit ε of K is given; and for sixteen types of four series of quadratic function fields K , the fundamental unit ε is exhibited explicitly.
对于实二次代数函数域K,给出了求K的基本单位ε的一个方法。
It is given that twonew solving methods,the first method proves that an algebraic function is a solution withthe help of analytic exfension and using the value of many--valued analytic function is different on the two sides of the fracture, then second method is obtained.
本文给出应用解析开拓证明了解是代数函数的一个新解法以及利用多值解析函数在裂纹两侧取不同值的方法导出了另一新解法。