湖北师范学院学报：自然科学版
湖北師範學院學報：自然科學版
호북사범학원학보：자연과학판
Journal of Hubei Normal University(Natural Science)
2012年
4期
1-3
,共3页
有限域%线性q-相伴多项式%不可约多项式%本原多项式
有限域%線性q-相伴多項式%不可約多項式%本原多項式
유한역%선성q-상반다항식%불가약다항식%본원다항식
finite fields%linearized q-associate polynomials%irreducible polynomials%primitive polynomials
先探讨利用有限域上线性q-相伴多项式由低次不可约或本原多项式构造高次不可约多项式或本原多项式。其次证明多项式与其线性q-相伴多项式的整除关系等价,通过求次数低的多项式的最大公因式,给出他们的线性q-相伴多项式的最大公因式,比直接求高次数的线性q-相伴多项式的最大公因式大大减少了计算量。
先探討利用有限域上線性q-相伴多項式由低次不可約或本原多項式構造高次不可約多項式或本原多項式。其次證明多項式與其線性q-相伴多項式的整除關繫等價,通過求次數低的多項式的最大公因式,給齣他們的線性q-相伴多項式的最大公因式,比直接求高次數的線性q-相伴多項式的最大公因式大大減少瞭計算量。
선탐토이용유한역상선성q-상반다항식유저차불가약혹본원다항식구조고차불가약다항식혹본원다항식。기차증명다항식여기선성q-상반다항식적정제관계등개,통과구차수저적다항식적최대공인식,급출타문적선성q-상반다항식적최대공인식,비직접구고차수적선성q-상반다항식적최대공인식대대감소료계산량。
In this paper,construction some irreducible polynomials or primitive polynomials with higher degrees through some ones with lower degrees were firstly discussed by linearized q-associate polynomials over finite field.Then the equivalence of divisibility between polynomials and their linearized q-associate polynomials was proofed.The greatest common factor of polynomials gave that of their linearized q-associate polynomials,which reduced the labor of calculation the greatest common factor directly.
