Irreducible polynomials over GF(2) with three prescribed coefficients

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....

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Bibliographic Details
Published in:Finite fields and their applications 2003-07, Vol.9 (3), p.286-299
Main Authors: Fitzgerald, Robert W., Yucas, Joseph L.
Format: Article
Language:English
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Summary: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.
ISSN:1071-5797
1090-2465
DOI:10.1016/S1071-5797(03)00005-4