1. The generator polynomial of a (15,11) Hamming code is defined by
Develop the encoder and syndrome calculator for this code, using a systematic form for the code
2. Consider the (15,4) maximal-length code that is the dual of the (15,11) Hamming code of Problem.
Find the generator polynomial g(X); hence, determine the output sequence assuming the initial state 0001. Confirm the validity of your result by cycling the initial state through the encoder.