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....

Full description

Saved in:
Bibliographic Details
Published in:Discrete mathematics 2004-01, Vol.274 (1), p.265-279
Main Authors: Yucas, Joseph L., Mullen, Gary L.
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Finite fields
Irreducible polynomials
Mathematics
Number theory
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(03)00092-X