Question

Let g(x)=x³ + x² + 1. Consider the information bits (1, 0, 1, 0, 1, 0, 1). Show the calculation to find the codeword if g(x) is used as the generating polynomial.

Answer 1

To find the codeword using the generating polynomial g(x) = x³ + x² + 1 and the information bits (1, 0, 1, 0, 1, 0, 1), we need to use polynomial long division. The codeword is (x⁶ + x⁴ + x + 1).

Step-by-step explanation:

To find the codeword using the generating polynomial g(x) = x³ + x² + 1 and the information bits (1, 0, 1, 0, 1, 0, 1), we need to use polynomial long division. To find the codeword using the generating polynomial g(x) = x³ + x² + 1 and the information bits (1, 0, 1, 0, 1, 0, 1), we need to use polynomial long division. The codeword is (x⁶ + x⁴ + x + 1).

First, arrange the information bits as a polynomial, in this case, we have x⁶ + x⁴ + x² + 1. Divide this polynomial by g(x) using long division:

x³ + x² + 1

x⁶ + x⁴ + x² + 1

Subtracting (x³ + x² + 1) from (x⁶ + x⁴ + x² + 1) gives us x⁶ + x⁴ + x + 1. The remainder x + 1 is the codeword. Therefore, the codeword is (x⁶ + x⁴ + x + 1).