Solve the following problem:
The parity check matrix of a linear block code is given below:
1. Determine the generator matrix for this code in the systematic form.
2. How many code words are in this code? What is the dmin for this code?
3. What is the coding gain for this code (soft decision decoding and BPSK modulation over an AWGN channel are assumed)?
4. Using hard decision decoding, how many errors can this code correct?
5. Show that any two code words of this code are orthogonal, and in particular any codeword is orthogonal to itself.