Finding dfree for the code

Question

Response to the following problem:   

A k = 1, K = 3, and n = 2 convolutional code is characterized by g₁ = [001] and g₂ = [110].

1. Find the transfer function of the code in the form T (Y, Z).

2. Is this code catastrophic? Why?

3. Find dfree for the code.

4. If the code is used on an AWGN channel using BPSK with hard decision Viterbi decoding, assuming E_b/N₀ = 12.6 dB, find an upper bound on the average bit error probability of the code.