Question: Please solve all parts for the below question Topic: coding theory (a) Write down a parity-check matrix for Ham(3,3). (b) What are the values of

Please solve all parts for the below question

Topic: coding theory (a) Write down a parity-check matrix for Ham(3,3). (b) What are the

(a) Write down a parity-check matrix for Ham(3,3). (b) What are the values of the parameters n, M, d, k, r and q for Ham(3.3)? Explain your answers and state the meaning of each parameter. (c) Write down a generator matrix for Ham (3,3), in standard form. (d) If one were to list the cosets for Ham(3.3), how many cosets would there be? How many syndromes would there be? How many members would there be in each coset? (e) Suppose that the message 1021102211201 is received across the noisy channel. What is the most likely original message (from before the parity-check digits were added)?

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