Determine the generator matrix for the coder illustrated in Figure 12.15. Use the generator matrix to generate the complete set of code words and use the results to check the code words shown in Figure 12.15. Show that these code words constitute a cyclic code.

Figure 12.15

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Output S2 S3 Input B Code words Register contents for input 0000000 word 1101 1000101 1100010 1110100 Shift Register content Output 100 1111111 0001011 110 0011101 3 111 0111010 4 111 Switch set to position B 011 001 1011000 1101001- 5 1001110 0110001 000 0100111 0010110 0101100 1010011