Question: Although it can be formally proved that the code in Table 10.3 is both linear and cyclic, use only two tests to partially prove the

Although it can be formally proved that the code in Table 10.3 is both linear and cyclic, use only two tests to partially prove the fact:

Table 10.3

Dataword Codeword Codeword Dataword 0000 0000000 1000 1000101 0001 0001011 1001 1001110 0010 0010110 1010 1010011 0011 0

a. Test the cyclic property on codeword 0101100.
b. Test the linear property on codewords 0010110 and 1111111.

Dataword Codeword Codeword Dataword 0000 0000000 1000 1000101 0001 0001011 1001 1001110 0010 0010110 1010 1010011 0011 0011101 1011 1011000 0100 0100111 1100 1100010 0101 0101100 1101 1101001 0110001 0110 1110 1110100 0111 0111010 1111 1111111

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