Find the transfer function of the code

Question

Solve the following problem:

Repeat Problem 1 for a code with

g₁ = [110],      g_{2 =}  [101],     g_{3 =} [111]

Problem 1: A con volutional code is described by

g₁ = [101],      g_{2 =} [111],     g_{3 =} [111]

1. Draw the encoder corresponding to this code.

2. Draw the state-transition diagram for this code.

3. Draw the trellis diagram for this code.

4. Find the transfer function and the free distance of this code.

5. Verify whether or not this code is catastrophic.