An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary field

Abstract

We establish a formula for the number of irreducible polynomialsf(x) over the binary fieldF 2 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 overF 2 of arbitrarily large degrees.

DOI: 10.1007/BF01810295

Cite this paper

@article{Niederreiter1990AnEF, title={An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary field}, author={Harald Niederreiter}, journal={Applicable Algebra in Engineering, Communication and Computing}, year={1990}, volume={1}, pages={119-124} }