代数几何

本文根据代数几何码的特点，设计了一个（k，m，n）密钥共享系统，使这个系统既具有共享系统的特点又具有纠错能力。

An ( k , m , n ) secret sharing system with the ability of correcting errors is designed based on algebraic-geometric codes .

基于FIA的代数几何码的译码

On the decoding of Algebraic Geometric Codes Based on FIA

再经过Jacobi反演，获得孤子方程的代数几何解。

The algebraic geometry solutions of these new soliton equations are obtained with the help of Jacobi inversion .

文章描述了代数几何与ECC的数学基础，讨论了椭圆曲线离散对数困难性问题及ECC在电子商务中的安全应用。

This paper describes the mathematics base of algebraic geometry and ECC . This paper also discusses the Elliptic curve discrete logarithm problem ( ECDLP ) and the security applications of ECC on E_commerce .

具体研究工作如下：1.基于纠错码的公钥密码体制的研究工作主要包括：（1）现有代数几何码的译码算法主要集中于一点代数几何码，为此，Xing针对广义RS码给出译码算法。

Researches on public-key cryptosystem based on error correcting codes include : ( 1 ) Existing decoding algorithms of algebraic-geometric codes mainly focused on one-point algebraic-geometric code , therefore , Xing gave a decoding algorithm of generalized RS codes .

代数几何理论在多元插值中的应用

The Application of Algebraic Geometry on Interpolation in Several Variables

关于代数几何中几个同调群的计算

About the calculation of several homology groups in algebraic geometry

线性系统同时极点配置的代数几何方法

Algebraic geometric method of simultaneous pole assignment of linear systems

拓扑，遍历理论，实代数几何。

Topology , Ergodic Theory , Real Algebraic Geometry .

本文重点考察了代数几何码译码算法的两个典型代表&Ehrhard译码算法和大数表决方案。

Two representatives are discussed primarily of decoding algorithms of algebraic geometric codes .

代数几何码译码算法纵览

A Survey on Decoding Algorithms of Algebraic Geometric Codes

序列综合与一类代数几何码的有效译码

Synthesis of Sequences and Efficient Decoding for a Class of Algebraic Geometry Codes

最后，给出了一点代数几何码的一个有效译码算法。

Lastly an efficient decoding algorithm is presented for one point algebraic-geometric codes .

基于代数几何码的密钥共享系统

A secret sharing system basing on algebraic-geometric codes

它由两个方面发展而来，代数几何和代数数论。

It has developed from two sources : algebraic geometry and algebraic member theory .

第二章介绍了代数几何的一些相关的理论。

In the second chapter , we introduce in brief the theory about algebraic geometry .

利用计算代数几何工具，研究了平面截口的隐式代数曲面的光滑拼接问题。

Studed the blending of implicit algebraic surfaces with the intersections on planes by using algebraic geometry .

数量和空间在解析几何，微分几何和代数几何中都发挥作用。

Quantity and space both play a role in analytic geometry , differential geometry , and algebraic geometry .

同一点代数几何码译码相比该译码算法更为一般，且算法简单，便于理解与实现。

Differed from the traditional decoding algorithm of one-point algebraic-geometric codes , this decoding algorithm is more general .

本文讨论了一类具有好的渐近参数的代数几何码。

In this paper , we discuss a class of algebraic geometry codes ( A-G codes ) with good asymptotic parameters .

本文借助于代数几何技巧构造了具有三次代数精度的基函数。

In this paper is given the construction of basis functions with accuracy up to degree three by the algebraic geometry technique .

文中算法还可用于求解一类代数几何码的快速译码问题。

The new algorithm can be used to deduce an efficient decoding for a class of algebraic geometry codes constructed by Justesen .

教程算术的让皮埃尔塞尔反映了这种用法，因为这样的短语，一阶算术或算术代数几何。

Course in Arithmetic by Jean-Pierre Serre reflects this usage , as do such phrases as first order arithmetic or arithmetical algebraic geometry .

引入了一些新的概念和观点使函数微分（导数）具有直观的代数几何表示。

Some new concepts and view are introduced as a result the derivatives of functions have corresponding simple multi-index interpretations and geometry partners .

本文利用计算代数几何工具，研究了平面截口处的一类具有隐式GC~1连续的混合代数曲面的构造。

In this article we will study the constructive theory of a kind of implicit GC ~ 1 blending algebraic surfaces by using algebraic geometry .

主要讨论了一点代数几何码的伴随式阵列及其上的线性递推关系。

The syndrome arrays are discussed in detail which are employed in decoding of a class of algebraic geometric codes and the linear recurring relations on that .

它们在函数逼近、计算几何、有限元以及代数几何等领域都占有重要的地位，同时具有广泛的应用。

They are important and have been widely applied in many fields such as function approximation , computational geometry , finite element , algebraic geometry and so on .

向量是现代数学中重要和基本的数学概念之一，是沟通代数几何与三角函数的一种重要工具和桥梁，同时也是一种重要的数学语言，同时还广泛应用于物理和科技领域。

Vector is one of the significant and basic conceptions in contemporary mathematics , which also acts as an important tool and bridge between algebraic geometry and trigonometric function .

他的研究领域是代数几何，这个数学分支后来成了剑桥的中坚，但却一直没有引起艾伦的兴趣，他们的之前的发展道路没有交点。

His field was algebraic geometry , a branch of mathematics then strongly represented at Cambridge , but one which never attracted Alan ; their paths had not crossed before .

并应用模论、理想论与代数几何的方法得到了这两种能达能观性的简单判据以及用补偿器综合稳定系统的充分条件。

By the methods of module theory , ideal theory and algebraic geometry , simple criteria for these reachability and observability , and the sufficient conditions for stabilizing the system are obtained .