# Element in finite field

• Feb 19th 2009, 05:18 AM
classic_phohe
Element in finite field
Is the elements in GF((2^2)^2) same as the elements in GF(2^4) ? and why is that so?
• Feb 19th 2009, 09:02 AM
ThePerfectHacker
Quote:

Originally Posted by classic_phohe
Is the elements in GF((2^2)^2) same as the elements in GF(2^4) ? and why is that so?

The notation GF(2^4) is already an ambiguous notation because it does not refer to any specific field. It happens to be that all fields of 16 elements are isomorphic to eachother and so we say "the" field of 16 elements if GF(2^4) however the elements may be totally distinct.
• Feb 19th 2009, 04:33 PM
classic_phohe
Quote:

Originally Posted by ThePerfectHacker
The notation GF(2^4) is already an ambiguous notation because it does not refer to any specific field. It happens to be that all fields of 16 elements are isomorphic to eachother and so we say "the" field of 16 elements if GF(2^4) however the elements may be totally distinct.

what about if i have GF(2^2) map to GF((2^2)^2) using irreducible polynomial either x^2+x+2 or x^2+x+3. What are the irreducible polynomial i can use to map GF((2^2)^2) to GF(((2^2)^2)^2) ?