consider the field F_2^4, defined by using polynomial representation with the irreducible polynomial f(x) = x^4 + x + 1.
Given element g = (0010) as a generator for the field. How are the powers of g generated? What are the steps to generate the binary values of g0 to g15 as follows?
g0 = (0001) g1 = (0010) g2 = (0100) g3 = (1000) g4 = (0011) g5 = (0110)
g6 = (1100) g7 = (1011) g8 = (0101) g9 = (1010) g10 = (0111) g11 = (1110)
g12 = (1111) g13 = (1101) g14 = (1001) g15 = (0001)