Here is my problem:

Say if I have a irreducible polynomial for that is , (N = elements of ) how do I determine the possible values of N ? Given the irreducible polynomial for is

thanks alot!

- April 2nd 2009, 06:07 PMclassic_phoheHow to determine coefficient in irreducible polynomial? HELP!!
Here is my problem:

Say if I have a irreducible polynomial for that is , (N = elements of ) how do I determine the possible values of N ? Given the irreducible polynomial for is

thanks alot! - April 2nd 2009, 07:49 PMThePerfectHacker
- April 2nd 2009, 10:40 PMclassic_phohe

can I conclude that N can only either be 1 or 3 which is and ?

but I realize if I would like to derive elements of field 16 using that irreducible polynomial , it cant be done.

unless I use then only I can produce 16 elements from the polynomials.

can you guide/advise me with this? - April 3rd 2009, 10:51 AMThePerfectHacker
- April 3rd 2009, 06:17 PMclassic_phohe
Ok! I agree what you explained. Now let sat I choose to be the irreducible polynomial, hence I use this to produce the elements in field of 16:

From there Im stuck. Can you give some tips how should I proceed with this? or I have already done wrongly at the first place?! - April 3rd 2009, 09:13 PMThePerfectHacker
- April 4th 2009, 10:59 PMclassic_phohe
- April 5th 2009, 01:33 PMThePerfectHacker
The field with 16 elements is the set where is the equivalent class modulo . Notice that where is the equivalence class of modulo and is the equivalence class of modulo . Thus, what I am saying is that let then every element has form (here we thinking of as an entire equivalence class).

- April 5th 2009, 04:27 PMclassic_phohe
thank you very much!!!

so field with 16 elements is the set so I will have 16 combination of A and B and hence produce 16 elements of field 16 with modulo the irreducible polynomial ; as .

let say I proceed to field 256, I have the irreducible polynomial as and I just use the same method you mentioned earlier reply to determine the possible value of ?

then I shall have the elements define as ? - April 5th 2009, 10:18 PMclassic_phohe
I believe the one you explain to me are all in polynomial basis. What if I would like to use Normal basis? Can you brief me how can it be done??

And also, the 16 elements produced by are in polynomial forms, each of them represent number from 0 to 15 right? let say i would like to identify number 2 and 14, is there any direct way to find which element representations are they in?