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According to the Galois extension theory of the number field,the discriminant of the field and the integral basis theory,the necessary and sufficient condition is attained which is m≡n≡1(mod4),where m and n are two different rational integers without square factors.

四次域是重要的Galois数域之一，该文对四次域Q进行了讨论；利用Galois扩张、域的判别式及整基等一些理论，得出了其具有正规整基的充要条件为m≡n≡1(mod4)(其中m，n是2个不同的无平方因子有理整数)。

Every Galois field has at least one primitive field element.

所有的Galois 域至少有一个本原域元素。

The proposed basis transformation approach from Galois Field (28) to Galois Field (24) can significantly reduce the hardware complexity of the Substitution Byte function.

根据所提出将基底从伽罗瓦场(28)转换至伽罗瓦场(24)方法，能够大大的减少取代位元组函数的硬体复杂度。

The elements in Galois field can be represented in several kinds of basis.In this paper,a Galois field elements are represented first by a polynomial basis.

在RS码的编译码电路中，主要涉及的基本运算电路单元是有限域的加法与乘法运算，其中对译码器性能影响较大的是乘法器的选择与设计。

The arithmetic operations in Galois field is central in the implementation of Reed-Solomon coders,storage and cryptographic algorithms.Multiplication is the most complicated arithmetic operation in Galois field.

1引言纠错编码技术在卫星通信、移动通信、数据存储、以及加密等领域已广泛应用，其中Reed-Solo-mon码是最重要的、也是研究最多的码类之一，已被多个国际标准采用。

This paper analysis the elliptic curves operation rules,presents a high speed serial-parallel elliptic curve multiplier for the Galois field GF(2^N) which based on optimal normal basis, compares the ECC chip speed and hardware resource consuming induced by the different Field partition.

本文分析了GF(2^N)域上的椭圆曲线的运算法则，提出了一种串－并行结构的基于优化正规基的高速有限域运算单元，比较了域划分D对芯片实现速度和硬件资源占用的影响，完成了域GF(2^N)上基于ONB的ECC芯片快速实现。

Three network coding protocols, i.e., non-regenerative network coding protocol, regenerative complex field network coding protocol and regener-ative Galois field network coding protocol are proposed and applied to the multicastnetwork to enhance the throughput.

然后，本文研究了两源、两宿、单中继的协作组播网络，提出了三种网络编码协议，即非再生网络编码(Non-Regenerative NetworkCoding，NRNC)、复数域再生网络编码(Regenerative Complex FiledNetwork Coding，RCNC)和伽罗华域再生网络编码(Regenerative GaloisFiled Network Coding，RGNC)。

Week 10 Conductor in static electric field, capacitor and capacity of conductor, dielectric in static electric field, Gauss theorem in dielectric medium.

第10周静电场中的导体、电容器和导体的电容；静电场中的电介质、有介质时的高斯定理。

Gauss theorem in magnetic field and Ampere cycle theorem, Ampere law, action of magnetic field to current line, cycle and charge in which.

磁场中的高斯定理和安培环路定理；安培定律。磁场对载流导线和载流线圈及对运动电荷的作用。

Week 2 Gauss theorem in magnetic field and Ampere cycle theorem, Ampere law, action of magnetic field to current line, cycle and charge in which.

第2周 磁场中的高斯定理和安培环路定理；安培定律。磁场对载流导线和载流线圈及对运动电荷的作用。

Researches reveal that students who suffer from corporal punishment tend to resort to violence in their future life.

研究表明遭受过肉体惩罚的孩子倾向于在他们今后的人生中使用暴力。

Total sugar of sarcocarp and chlorophyll of pericarp increased firstly, and then decreased afterward along with altitude; Titratable acidity, ascorbicacid and anthocyanin of pericarp were increased along with altitude; The content of protein increased firstly and decreased afterward along with altitude; Carotenoid of pericarp were decreased along with altitude.

果肉总糖和果皮叶绿素含量随海拔高度升高先升高后降低；可滴定酸、维生素C和果皮花青苷含量均随海拔升高而升高；蛋白质在1720m处最大，1420m处最小；果皮类胡萝卜素随海拔升高而降低。