http://techrept.petermmaurer.comQuick BlogcastSun, 12 Feb 2012 00:39:43 GMThttp://techrept.petermmaurer.com/2007/02/01/note-solutions-of-a-quartic-gf2-polynomial.aspx#comment-244339Peter M. MaurerSometimes it pays to take look back at the book before exerting a lot of effort. If p is any irreducible polynomial of degree m over GF(2), and a is any root of p, then GF(2^m) has basis vectors 1, a, a^2, ... , a^m-1. Furthermore, the complete list of roots of p is a, a^2, a^4, a^8, ... a^2^i, a^2^m-1. Thus, for every irreducible polynomial p over GF(2) a being a root of p also implies that a^2 is a root of p. Since the roots of p are mathematically indistinguishable, every square of every eigenvalue of a GF(2) matrix is also an eigenvalue of the same matrix.http://techrept.petermmaurer.com/2007/02/01/note-solutions-of-a-quartic-gf2-polynomial.aspx#comment-244339Mon, 05 Feb 2007 03:51:43 GMT