Factorization of polynomials over finite fields

If f(x) is a polynomial over GF(q), we observe (as has Berlekamp) that if h(x)2 =_h(x) (modf(x)), thenf(x) = IHa eGF(q) gcd (f(x), h(x) a). The object of this paper is to give an explicit construction of enough such h's so that the repeated application of this result will succeed in separating all irreducible factors of f. The h's chosen are loosely defined by hi(x) = xi + xiq + xiq2 + * * * (mod f(x)). A detailed example over GF(2) is given, and a table of the factors of the cyclotomic polynomials 4b(x) (mod p) for p = 2, n < 250; p = 3, n < 100; p = 5, 7, n < 50, is included.