有限域上线性q-相伴多项式及其应用

Linearized q-associate polynomials over finite field F_q and their properties

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。

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.