[GAP Forum] Finite fields

[comptel]

hi,
I
I have some doubts on finite fields. Can anyone answer the following question?
 
we wish to encode the message using  F32... Define the cumulative degree of a polynomial to be the sum of degrees of its monomials.
 
a)How many irreducible polynomials of degree 5 over Z/2Z are there?
what are they?
 
 
b)
Let Y be a root of the irreducible polynomial of degree 5 of lowest cumulative degree. Then { 1,Y,Y^2,Y^3,Y^4} forms a basis for F32 over Z/2Z. Writing each element  of F32 as a 5 tuple with respect to this basis, find all the powers of Y.
 
c) We encode message (numbers between 0 and 31) by raising it Y to that power and then returning the five-bit binary representation we get when writing this element as a 5-tuple with respect to {1,Y,Y^2,Y^3,Y^4}.If 19 is the result m then what number was initially sent?.
 
 can anyone help ?.
 


		
---------------------------------
Do you Yahoo!?
 Yahoo! Search presents - Jib Jab's 'Second Term'