The parity check matrix of a linear block code C(7, 4) is given as
H =
(a) Find the generator matrix in systematic form.
(b) Find the minimum distance of the code using the parity check matrix.
(c) Decide on the error detection and correction capability of this code.
(d) Let tc be the number of bit errors that the code can correct. Determine the number of words inside a Hamming sphere of radius tc; at the center of the sphere, a code-word exists.
(e) Construct the syndrome table of this code.
(f) Extend this code to a C(8, 4) linear block code. Find the generator and parity