1. Using p(x) = x2 + x + 1, construct GF(22). Find all the conjugate classes; calculate the minimal polynomials. 2. Solve the equation set α3 x + αy = α2 α5 x + α2 y = α4 in GF(23). Use p(x) = x3 + x...

1. Using
p(x)
= x²
+ x + 1, construct
GF(2²
).
Find all the conjugate classes; calculate the minimal polynomials.

2. Solve the equation set

α³
x + αy = α²

α⁵
x + α²
y = α⁴

in
GF(2³). Use
p(x) = x³
+ x + 1 as your primitive polynomial.