1. Not finding help here? Sign up for a free 30min 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!

Irreducible Polynomials p 5 degree 4

  1. Nov 8, 2007 #1
    I am attempting to construct a field containing 625 elements and should be in the form Zn[x] mod f(x).

    Factoring 625 leads to 5^4. So I'm guessing my field will be GF(5^4). So in order for me to construct a field with all elements in it, I need f(x) to be some irreducible polynomial mod 5 of degree 4.

    How can I go about finding irreducible polynomials? I know I can choose all the polynomials below degree 4 with coefficients mod 5 and attempt to find one without factors, but that would take forever. Is there a quick way to do this or a list of precomputed irreducible polynomials given GF(p^n) where p is prime and n is greater than 1??

    Thanks.
     
  2. jcsd
  3. Nov 9, 2007 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    I can't imagine anyone's bothered to precompute anything. The solution is to think about F_5, the field with 5 elements, and decide if you know any polynomial that every element of F_5 satisfies.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?