Irreducible polynomials over GF(2) with three prescribed coefficients

Authors:
Robert W. Fitzgerald;Joseph L. Yucas
Affiliations:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, USA;Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, USA
Venue:
Finite Fields and Their Applications
Year:
2003

Citing 1
Cited 2

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Abstract

For an odd 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.