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SWAN-LIKE REDUCIBILITY FOR TYPE I PENTANOMIALS OVER A BINARY FIELD


RYUL KIM, SU-YONG PAK AND MYONG-SON SIN
1,2,3. Faculty of Mathematics, Kim Il Sung University, Kumsong Street, Pyongyang, Democratic People's Republic of Korea,
Corresponding author: ryul kim@yahoo.com
Corresponding author: paksuyong@yahoo.com
Corresponding author: sinmyongson@yahoo.com

Issue:

SSRSMI, Number 1, Volume XXIV

Section:

Volume 24, Number 1

Abstract:

Swan (Pacific J. Math. 12(3) (1962), 1099-1106) characterized the parity of the number of irreducible factors of trinomials over F2. 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) = xm + xn+1 + xn + x + 1 over F2 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.

Keywords:

phrases: finite field, type I pentanomial, discriminant, resultant.

Code [ID]:

SSRSMI20140124V24S01A0003 [0004060]

Full paper:

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