二元域上I型五项式的Swan型约化
Swan-like reducibility for Type I pentanomials over a binary field
摘要：
Swan（Pacific J. Math. 12（3）（1962），1099-1106）刻画了$F_2$上三项式的不可约因子个数的奇偶性。近年来，许多学者在确定有限域上多项式约化的问题上得到了Swan式的结果。本文确定了$n$为偶数的$F_2$上的I型五项$f(x)=x^m+x^{n+1}+x^n+x+1$的不可约因子个数的奇偶性.我们的结果是基于Stickelberger-Swan定理和牛顿公式，这是非常有用的多项式的判别式的计算。
英文摘要：
Swan (Pacific J. Math. 12(3) (1962), 1099-1106) characterized the parity of the number of irreducible factors of trinomials over $F_2$. Many researchers have recently obtained Swan-like results on determining the reducibility of polynomials over finite fields. In this paper, we determine the parity of the number of irreducible factors for so-called Type I pentanomial $f(x)=x^m+x^{n+1}+x^n+x+1$ over $F_2$ with even $n$. Our result is based on the Stickelberger-Swan theorem and Newton's formula which is very useful for the computation of the discriminant of a polynomial.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
