Determining the minimum Hamming Distance

Question

How can I find the minimum Hamming Distance for the above?

I understand the string comparison idea and putting it into a table based on C0, C1, C2, etc but I'm not sure how to group the code above. Any suggestions? Thank you in advance.

Answer 1

Generally, to find the minimum Hamming distance you have to compute the Hamming distance of each pair of code words and then take the minimum of these. For special cases, e.g. linear codes there are theorems for quicker determination of the minimum Hamming distance (https://en.wikipedia.org/wiki/Linear_code).

In your example, the eye spots several adjacent code word pairs differing only in one bit, so as Egor wrote, the minimum Hamming distance is 1.