QUESTION 1 (15 marks) (i) A Hamming code is to be transmitted. If at least 7 data bits are needed for this code, find the values of and Hint: Try m=2,3, and 4 (ii) State two applications of Hamming codes (iii) Three code words in a particular block code are given by (a) What is the minimum Hamming weight for this set of code words? (6) How many errors can the code correct? (iv) The generator matrix G of a (7,4,3) Hamming code is given as 1100101 11 0101010 G 0011001 OOO0111 Swap columns 4 and 5 to create a new form of the matrix G. Explain the importance of presenting the generator matrix in this form and hence deduce the parity-check matrix H. QUESTION 1 (15 marks) (i) A Hamming code C(n,k) is to be transmitted. If at least 7 data bits are needed for this code, find the values of n and k. Hint: Try m=2,3, and 4 (ii) State two applications of Hamming codes (iii) Three code words in a particular block code are given by Ci = 1000111, C = 000 101 1 and Ck = 1011101 (a) What is the minimum Hamming weight for this set of code words? (b) How many errors can the code correct? (iv) The generator matrix G of a (7,4,3) Hamming code is given as i 0 0 1 0 1 1 0101010 0011001 0 0 0 0 1 1 1 Swap columns 4 and 5 to create a new form of the matrix G. Explain the importance of presenting the generator matrix in this form and hence deduce the parity-check matrix H