Consider a systematic (n, k) linear block code with parity check equations:
v0 = m0 + m1 + m3
v1 = m0 + m2 + m3
v2 = m0 + m1 + m2
v3 = m1 + m2 + m3
where mi is the message bits (i = 0, 1, 2, 3). Determine the following:
a. The parameters n and k. Construct the generator matrix for this code.
b. Show that this code is capable of correcting all single-bit errors in any received r.
c. Are the vectors r1 = [10101010] and r2 = [01011100] valid code-words?