Using the generator matrix of a (2 m − 1, m) maximum-length code as defined in Section 7.3–3,…

Using the generator matrix of a (2m − 1, m) maximum-length code as defined in Section 7.3–3, do the following

a. Show that maximum-length codes are constant-weight codes; i.e., all nonzero codewords of a (2m − 1, m) maximum-length code have weight 2m−1.

b. Show that the weight distribution function of a maximum-length code is given by Equation 7.3–4.

c. Use the MacWilliams identity to determine the weight distribution function of a (2m − 1, 2m − 1 − m) Hamming code as the dual to a maximum-length code.

 

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