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arXiv · 1406.7597

Swan-like reducibility for Type I pentanomials over a binary field

Ryul Kim·Su-Yong Pak·Myong-Son Sin
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Abstract

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.

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Ryul Kim, Su-Yong Pak, Myong-Son Sin. 2014-06-30. Swan-like reducibility for Type I pentanomials over a binary field. https://arxiv.org/abs/1406.7597

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