Develop a set of tables similar to Table 4.7 for \(\mathrm{GF}(4)\) with \(m(x)=x^{2}+x+1\).

Table 4.7 Polynomial Arithmetic Modulo (x 000 001 010 011 100 101 110 111 + 0 1 x x + 1 x x + 1 x + z x + x + 1 000 0 0 1 x x + 1 x x + 1 x + x x + x + 1 + x + 1) 001 1 1 0 x + 1 x x + 1 x + x + 1 x + x 010 X X x + 1 0 1 x + x x + x + 1 x x + 1 011 x + 1 x + 1 X 1 0 x + x + 1 x + x x + 1 x (a) Addition 100 x z.x x2 +1 x + x x + x + 1 0 1 X x + 1 101 x + 1 I + z z x + x + 1 x + 2x 1 0 x + 1 X 110 x + x x + 1 x + x + 1 x x2 +1 X x + 1 0 1 111 x + x + 1 x + x + 1 x + x x + 1 x x + 1 X 1 0