不可约多项式外文文献加翻译

不可约多项式外文文献加翻译
不可约多项式外文文献加翻译irreducible polynomial
Let f(x) = f1(x)l1…fk(x)lk be the standard factorization of f(x) in the polynomial ring F[x], where fi(x) is an irreducible polynomial with leading coefficient 1 and degree ni.
f(x)=f_1(x)~l1…f_k(x)~lk是f(x)在多项式环F[x]中的标准分解式,f_i(x)是最高系数为1、次数为n_i的不可约多项式.
In this note, we suppose n is a composite, Z_n is a residue class ring mod n, r(x)∈Z_n[x] and r(x) is a monic irreducible polynomial of degree k (k>0) over Z_n.
设n是一个合数,Z_n表示模n的剩余类环,r(x)∈Z_n[x]是一个首一的k(>0)次不可约多项式。

From these, the cyclic Zq? code with the generator hm(x) whichis primitive basic irreducible polynomial over Zq can be mapped for nonlinearcode with big distance over Zp.
由此将Zq上的一类由本原基本不可约多项式hm(x)生成的循环码映射成Zp上具有较大距离的非线性码,其中本原基本不可约多项式hm(x)是指
hm(x)在模p映射下的象hm(x)是Zp[x]中的本原多项式.
As a matter of fact, the method starts from Z_2, and there is an irreducible polynomial x~2+x+l over Z_2. As a generating element, which may be regarded as a Princpal Ideal (x~2+x+1). Therefore, as are know from the thory of Modern Algebra, Z_2[x]/(x~2+x+1) is a Finite Fields.
这一方法实质上是从Z_2出发,以Z_2上的一个不可约多项式
x~2+x+1为生成元做一个主理想(x~2+x+1),然后由近世代数的理论知
Z_2[x]/(x~2+x+1)是一个有限域,从而得到了GF(4)。

Irreducible Polynomial of Integral Coefficient
关于整系数不可约多项式
prime polynomial
This paper directly proves that a prime polynomial has the radical solutionsover a finite field.
直接证明了有限域上的不可约多项式有根号解
“不可约多项式”译为未确定词的双语例句
We give a definition for n is Generalized Carmichael Number of order k modulo r(x) and denote this by n∈C_(k,r(x)). So we give another definition: C_k={UC_(k,r(x))|r(x) are all monic irreducible polynomials of degree k (k>0) over Z_n}.
本文引入n是k阶摸r(x)的Carmichael数的定义,全体这样的数记为集C_(k,r)(x),由此给出k阶Carmichael数集:C_k={∪C_(k,r)(x)|r(x)过
全体Z_n上的首一k次不可约多项式}。

The Irreducible Polynomials over Finite Fields
有限域上的不可约多项式
In chapter 1, we suppose n is a compos-ite, Zn is residue class ring mod n, r(x) ∈Z_n[x] is a monic irreducible polynomialof degree k(k > 0).
在第一章中, 设n 是一个合数, Zn 表示模n 的剩余类环,r(x) ∈
Z_n[x] 是一个首一的k 次(k > 0) 不可约多项式.
We give a construction of perfect nonlinear mappings using generalized bent functions and irreducible polynomials over the finite field Z p.
在分组密码中 ,为了抗差分攻击 ,需要完美非线性映射 . 利用有限域 Zp上的广义 Bent函数和不可约多项式 ,给出了完美非线性映射的一类构造 .
To simplify reduction modulo, special polynomials are used to generate finite field GF(2m), such as AOP (all one polynomials) and trinomials.
为了简化模不可约多项式f(x)运算,采用特殊多项式
AOP(allonepolynomials)和三项式,产生有限域GF(2m)。