- #1
classic_phone
- 10
- 0
Here is my problem:
Say if I have a irreducible polynomial for [tex]GF(2^2)[/tex] that is [tex]x^2 + Nx + 1[/tex] , (N = elements of [tex]GF(2)[/tex]) how do I determine the possible values of N ? Given the irreducible polynomial for [tex]GF(2)[/tex] is [tex]x^2 + x + 1[/tex]
I think since the field is [tex]GF(4)[/tex] so we have choice of [tex]\{ 0,1, \alpha, \alpha + 1\}[/tex]
thus to make the polynomial irreducible N could be either 1 or 3 which is [tex]\alpha[/tex] or [tex]\alpha + 1[/tex].
so now i have polynomial of either [tex]x^2 + \alpha x + 1[/tex] or [tex]x^2 + (\alpha +1 )x + 1[/tex]
then how do I use the polynomial to generate the 16 elements for the field of [tex]GF((2^2)^2)[/tex] ?? please guide me with some steps.
thanks alot
Say if I have a irreducible polynomial for [tex]GF(2^2)[/tex] that is [tex]x^2 + Nx + 1[/tex] , (N = elements of [tex]GF(2)[/tex]) how do I determine the possible values of N ? Given the irreducible polynomial for [tex]GF(2)[/tex] is [tex]x^2 + x + 1[/tex]
I think since the field is [tex]GF(4)[/tex] so we have choice of [tex]\{ 0,1, \alpha, \alpha + 1\}[/tex]
thus to make the polynomial irreducible N could be either 1 or 3 which is [tex]\alpha[/tex] or [tex]\alpha + 1[/tex].
so now i have polynomial of either [tex]x^2 + \alpha x + 1[/tex] or [tex]x^2 + (\alpha +1 )x + 1[/tex]
then how do I use the polynomial to generate the 16 elements for the field of [tex]GF((2^2)^2)[/tex] ?? please guide me with some steps.
thanks alot