(50) Given the (7, 4) Hamming code parity check equations: aa az a = 0 aaa,a=0 [a a a = 0 a) (15) Please give the parity check matrix and its generator matrix b) (15) Suppose we have message m = 1010. What is the codeword after encoding? c) (10) In receiver side, in order to decode the received codeword to message, the syndromes are needed. Please calculate the syndromes for the error bits in each location. (fill them in the table below) S1 S2 S3 Error bit a a2 a4 as a6 No error d) (10) Now, suppose the codeword received by the decoder is 1010000. What is the most likely transmitted message m?