Chapter 3 introduces the correcting ability of the rs code . then it particularly states the definition and algorithm of galois field , and analyses the realization of the limited field multiplier based on the dual basis 第三章分析讨论了rs码的特点,给出了伽罗华有限域的定义与运算规则,推导和分析了基于对偶基的有限域乘法器实现方法。
- all of the cyclic codes over the galois ring gr ( 4m ) , and the bases for gr ( 4m ) over z4 are determined , such that with respect to the bases , the 4 - ary image of the cyclic codes are still cyclic 对于伽罗华环gr ( 4 ~ m )上的一类循环码，以及gr ( 4 ~ m )在z _ 4上的一组基，给出了满足这类循环码相对于该组基展开后得到的码是四元循环码的充分必要条件，该条件简便实用； 5
Then we show an algorithm design of the elliptic curve crypto based on galois field . as a main part , the design theory and concrete solution of it are presented step by step , ic chip design method for implementation of the algorithm is described in detail 设计完成了一种基于有限域的椭圆曲线加密算法，主要包括适合于168bit椭圆曲线加密的有限域乘法、加法、除法器的实现； 4
This thesis is composed of following parts : the fundamental theory of the modern cryptology is briefly researched , in which the mathematic model of cryptology , data encrypt principle and galois field theory related with elliptic curve crypto is discussed 论文的主要内容为： 1研究了现代密码学相关的基本理论，介绍了密码系统的数学模型、数据加密原理和与椭圆曲线加密密切相关的有限域理论； 2
We define a frobenius map over galois , trace codes and subring subcode . we prove the trace of dual codes over galois is the dual codes of subring subcode . all the results are very important for the study of the error correcting codes over rings 第四，作者在galois环gr ( q ~ m )上定义了frobenius映射，并在该环上定义了迹码和子环子码的概念，得到了galois环上的一个码的对偶码的迹码是该码的子环子码的对偶码。
For classification without class label , we discuss how to find a class attribute as a class label , and on this basis we then introduce support _ coefficient to construct approximate galois structure . , and extraction of classification rules has also been discussed 无确定类别属性的的分类问题讨论了类别属性的确定，以及根据确定的类别属性，在此基础之上引入支持率，讨论近似格的构造和有关近似格上规则求解的问题。
In the design and analysis of sequence cipher , we obtain the following results . first , we give the trace representation of primitive sequences and their corresponding highest lever sequences on galois ring by using the trace function theory and the characteristic of lever factorization , and determine the correlation function linear complexity and element distribution of the highest lever sequences of primitive sequences on galois ring gr ( 4 , m ) 在序列密码的设计和分析方面：首先，利用galois环上迹函数理论和本原序列的权位分解特征，给出了本原序列及其最高权位序列的迹表达式，然后利用galois域上二次型理论与指数和理论决定了特征为4的galois环上本原序列的最高权位的相关函数、线性复杂度和元素分布。
