1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook