Question 1: For a linear block code (n, k), the codeword (a 7-bit string) is defined as Vi = P1P2P3d1d2d3d4 (i = 1, ..., 2k) by using the corresponding 4-bit input string U did2d3d4 and the following parity equations: P1 = di o d2 dz P2 = di o d2 da P3 = di dz 0 d4. a) Determine n and k. b) Find the redundancy of the code and code rate. c) The relationship between any codeword and the generator matrix G, is given as Vi = UG. Determine G. d) Find all the codewords of the code. e) What is the minimum Hamming distance of the code? f) What are the error detection and error correction capabilities of the code? g) If 1010010 is received at the destination, what are the all possible input bit streams for ui? Determine and discuss whether the receiver can detect/correct the error (if any) in all cases. (HINT: Please first check whether the received bit stream is valid or not.)