Abstract
We establish a formula for the number of irreducible polynomialsf(x) over the binary fieldF2 of given degreen ≧ 2 for which the coefficient ofx n-1 and ofx is equal to 1. This formula shows that the number of such polynomials is positive for alln ≧ 2 withn ≠ 3. These polynomials can be applied in a construction of irreducible self-reciprocal polynomials overF2 of arbitrarily large degrees.
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