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