1. Decide whether the polynomials X4+x+1 x4+x3+x+1 are irreducible polynomials or not. 2. Construct the extended field GF(24) using the primitive polynomial p(x) = x4 + x3 + 1. Repeat the...

1. Decide whether the polynomials

X⁴+x+1 x⁴+x³+x+1

are irreducible polynomials or not.

2. Construct the extended field
GF(2⁴) using the primitive polynomial p(x) = x⁴
+ x³
+ 1. Repeat the construction process using the primitive polynomial
p(x) = x²
+ x + 1. Comment on the field elements for both constructions.