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.
Cuvinte cheie
phrases: finite field
type I pentanomial
discriminant
resultant.