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) = fl (x)ll--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_l (x) 1・・・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) WZ_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) EZ_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 met hod starts from Z_2, and t here 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+l). Therefore, as are know from the thory of Modern Algebra, Z_2[x]/(x~2+x+l) is a Finite Fields.
这一方法实质上是从Z_2岀发，以Z_2上的一个不可约多项式x~2+x+l 为生成元做一个主理想(x~2+x+l),然后由近世代数的理论知Z_2[x]/(x~2+x+l)是一个有限域，从而得到了GF⑷。

Irreducible Polynomial of Integral Coefficient
关于整系数不可约多项式
a 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
Q “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 nWC_(k, r(x))・ So we give another definition：C_k二{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= {UC_(k, r) (x) |r(x)i± 全体Z_n上的首一k次不可约多项式｝o
The Irreducible Polynomials over Finite Fields
有限域上的不可约多项式
In chap ter 1> we suppose n is a compos-ite, Zn is residue class ring mod n, r (x) WZ_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) W Z_n[x]是一个首一的k次(k > 0)不可约多项式.
We give a construetion of perfect nonlinew 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 (allonepo 1 ynomia 1 s)和三项式，产生有限域GF(2m)。