binary trace

*To*: mathgroup at smc.vnet.net*Subject*: [mg43738] binary trace*From*: Khanh <bbking1981 at mail.ru>*Date*: Thu, 2 Oct 2003 02:52:05 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi there! I don't realy under stand the meaning of the term "binary Trace" used in Finite Field and its use in determining the cofficients of a minimal polynomial. Eg: n==3 so i have a minimal poly in GF(2) is F(x)==(x+a)(x+a^2)(x+a^4) with a is a element of GF(2^3) and is root of F(x) so F(x)==x^3+ x^2(a+a^2+a^4)+x(a^3+a^6+a^5)+a^7 ==x^3+x^2*T(a)+x*T(a^3)+T(a^7) here T(a)is trace of a But how can i determine the values of T(a),T(a^3),T(a^7) to determine F(x) Can somebody help me to explain that?I would aprreciate it very much.Thanks a lot. Khanh