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MathGroup Archive 2003

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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






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