Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = aX7...

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Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = a³X7 +aX6 + a²X4+ a²X² + a¹¹X + 1 over GF (24) by the polynomial g(X) = X¹ + a³X² +a5X + 1 over GF (24). Find the quotient and the remainder (use Table 1) Table 1: Three representations for the elements in GF (24) generated by p(X) = 1 + X+X4. Power representation 0 1 α¹ a² a³ 4 a a5 α6 a7 α8 α⁹ a10 a¹1 12 α a13 14 α· 0 1 Polynomial representation α a² a³ 1 + a a + a² a² + a³ 1 +a+a³ 1 + a² a + a³ 1+ a + a² a + a² + a³ 1+ a + a² + a³ 1 + a² + a³ 1 + a² 4-Tuple representation 0 1 0 0 0 1 0 اد 0 1 1 0 1 0 1 1 1 DITOOOO OOO 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 -OO 1 0 1 1 0 1 -110 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 Q2) Let a be a primitive element in GF (24). Divide the polynomial f(X) = a³X7 +aX6 + a²X4+ a²X² + a¹¹X + 1 over GF (24) by the polynomial g(X) = X¹ + a³X² +a5X + 1 over GF (24). Find the quotient and the remainder (use Table 1) Table 1: Three representations for the elements in GF (24) generated by p(X) = 1 + X+X4. Power representation 0 1 α¹ a² a³ 4 a a5 α6 a7 α8 α⁹ a10 a¹1 12 α a13 14 α· 0 1 Polynomial representation α a² a³ 1 + a a + a² a² + a³ 1 +a+a³ 1 + a² a + a³ 1+ a + a² a + a² + a³ 1+ a + a² + a³ 1 + a² + a³ 1 + a² 4-Tuple representation 0 1 0 0 0 1 0 اد 0 1 1 0 1 0 1 1 1 DITOOOO OOO 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 -OO 1 0 1 1 0 1 -110 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1

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To divide the polynomial fX X X aX X X 1 over GF2 ... View the full answer