1.Assume that the extended field GF(25). is constructed using the primitive polynomial p(x) = x5 + x3 Obtain the conjugates of α3 in GF(25)., and find the minimal polynomial for the obtained conjugate...

1.Assume that the extended field
GF(₂
⁵). is constructed using the primitive polynomial
p(x) = x5 + x3 Obtain the conjugates of α3 in
GF(₂
⁵)., and find the minimal polynomial for the obtained conjugate class.

2.Factorize x15 + 1.

3. Expand (x4 + α2x3 + α5x + α3)4 in
GF(₂
³).