Although it can be formally proved that the code in Table 10.3 is both linear and cyclic,

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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.

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