Advanced Search

Question: x^q-x=0 to "reduce" polynomial function of galois field

Question:x^q-x=0 to "reduce" polynomial function of galois field

gepo 541
student
March 21 2009
0

For a given galois field, suppose there is such a polynomial function mapping from GF(q) to GF(q):
x^(q+m)+x^(q+m-1)+x^(q+m-2)+...+x^(1).
I can use x^q-x=0 to "reduce" it to such the following form:
x^(q-1)+x^(q-2)+x^(q-3)+...+x^(1)

now, the problem is whether this is the only method (x^q-x=0) to reduce a polynomial function mapping from GF(q) to GF(q)?

Thanks a lot.
Please Wait...