Solve the following problem:
The generator matrix for a linear binary code is
![439_linear binary code.jpg](https://secure.tutorsglobe.com/CMSImages/439_linear binary code.jpg)
a. Express G in systematic [I|P] form.
b. Determine the parity check matrix H for the code.
c. Construct the table of syndromes for the code.
d. Determine the minimum distance of the code.
e. Demonstrate that the codeword c corresponding to the information sequence 101 satisfies cHt = 0.