A (15,11) linear block code can be defined by the following coefficient matrix 0 0 1 0 10 1 1 0 0 1 0 1 1 0 0 0 P =| 1 0 0 1perfect code if its standard array has all the error patterns of t and fewer errors and no others as coset leaders] |c. Suppo

A (15,11) linear block code can be defined by the following coefficient matrix 0 0 1 0 10 1 1 0 0 1 0 1 1 0 0 0 P =| 1 0 0 1 0 1 1 1 1 1 0 1 0 1 10 1 1 1 1 a. What is the parity check-check matrix for this code b. List the coset leaders from the standard array. Is this code a perfect code? Justify your answer. [A t-error correcting code is called a perfect code if its standard array has all the error patterns of t and fewer errors and no others as coset leaders] |c. Suppose the received vector is r= 01111 1001011011. Compute the syndrome. Assuming that a single bit error has been made, find the correct code word



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