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Arithmetic in Mathematical Fields (in particular GF(2^8) )

  1. Mar 22, 2010 #1
    1. The problem statement, all variables and given/known data

    * note that I meant fields in the abstract mathematical sense, notphysical (i.e. electric) fields! *

    Finding the determinant of a matrix in GF(28)

    I want to know if it is using mod 256 or mod 255 in the field of GF(28)

    2. Relevant equations

    Just math

    3. The attempt at a solution

    I found the determinant of a matrix no problem. Everything in between is all good. What I want to know is that in the field of GF(28), am I taking the number mod 255 or mod 256?

    I know that there are a total of 256 elements in the field, but I'm just not sure which mod to take for the final answer, since it is a negative determinant.
     
  2. jcsd
  3. Mar 22, 2010 #2

    Mark44

    Staff: Mentor

    Modulo 256. The possible moduli are 0, 1, 2, ..., 255, the possible remainders when you divide by 256.
     
  4. Mar 23, 2010 #3
    thanks Mark
     
  5. Mar 24, 2010 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Noooo! You're both wrong. GF(256) is a finite field, an extension field of GF(2). It is not not the same as the ring Z/256 of integers modulo 256.
     
  6. Mar 24, 2010 #5
    Hurkyl, I agree that GF(256) is a finite field, but if we're both wrong, then how would I handle whole negative numbers?
     
  7. Mar 24, 2010 #6
    You are just computing Mod 2 with the numbers. The elements are polynomials, the coefficients are from Z_2 and you're computing Modulo some primitive polynomial over Z_2 of 8th degree.
     
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