Irreducible polynomials over GF(2) with prescribed coefficients

For an even positive integer n, we determine formulas for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of x(n-1), x(n-2) and x(n-3) are specified in advance. Formulas for the number of elements in GF(2(n)) with the first three traces specified are also given. (C) 2003 Elsevier B.V. All rights reserved.