1. Decide whether the polynomial P(x) = x5 + x4 + x2 + x + 1 is a primitive polynomial or not. 2. Find all the conjugate classes of GF(25). How many minimal polynomials do we have in GF(25)? 3. Obtain...

1. Decide whether the polynomial

P(x) = x⁵
+ x⁴
+ x²
+ x + 1

is a primitive polynomial or not.

2. Find all the conjugate classes of
GF(₂
⁵). How many minimal polynomials do we have in
GF(2⁵)?

3. Obtain the binary representation of the polynomial

P(α) = α²
+ α

in
GF(₂
³) and
GF(₂
⁵).