Minimum Distance of Linear Binary Code

Question

I am new to understanding Coding Theory, and would not ask anybody just for the final answer, but rather the understanding/process.

Given an example question to calculate distance $(01010_2, 10101_2)$, I know the distance is based off the number of differences in $1$'s, equating to distance $= 5$.

However, how do I perform an operation to work out a "Minimum Distance" given a set $\{01010_2, 10101_2, 11011_2, 00100_2\}$? Would I do a similar operation as previously, but altogether at once?

Any illustration would greatly help me understand this.

Answer 1

1. The distance is based off the number of differences in entries, not just $1$'s.
2. For the minimum distance of a (small) given set: perform the distance operation to every distinct pair of words in the set; the minimum distance of your set will be the least number you compute.