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) = X4+ 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 a¹ q² a³ a4 as α6 a7 a8 a⁹ a 10 a11 a ¹. 12 a13 a¹4 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 0 00 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 blo 0 1 1 0 1 0 1 1 1 1 1 0 0 0 oooo 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1001 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) = X4+ 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 a¹ q² a³ a4 as α6 a7 a8 a⁹ a 10 a11 a ¹. 12 a13 a¹4 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 0 00 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 blo 0 1 1 0 1 0 1 1 1 1 1 0 0 0 oooo 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1001
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The task at hand involves dividing the polynomial fX 3X7 X6 7X4 2X2 11X 1 over GF24 by the polynomial gX X4 3X2 5X 1 also over GF24 Since the arithmet... View the full answer
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