1. (35 points total) Consider (8,4) code whose parity check equations are = Po m₁+m2 + m3. P1 mo+m1 + m2 P2 mo+m1 + m3. P3 mom2 + m3 (1) Where mo, m₁, m2, m3 are message bits, and Po, P1, P2, P3 are parity bits. (a) Find the systematic generator matrix, G, and parity check matrix, H, of this code? (b) Construct an encoder for the given code using only shift-registers (memory elements), exor, and, and or logic gates, gates can have any number of inputs? (c) Find the minimum distance of the code, dmin? (d) Identify how many errors can this code correct? (e) Identify how many errors can this code detect? (f) Identify how many errors can be corrected and detected simultaneously?