# How to build 4 codewords with a code distance of 5?

I wonder how can I construct 4 (distinct) codewords given the fact that code distance is 5. As far as I know that the code distance is the number of distinct bits between any 2 codewords. How to achieve this code distance for the 6 possible pairs from the 4 codewords available(of any bit length). I named, for example, codewords u, v, w, & x so d(u,v) = d(u,w) = d(u,x) = d(v,w) = d(v,x) = d(w,x) = 5. The code words must be in binary format i.e 00100 10011. I considered a code length of 10 to achieve this but still struggling to find a solution.

• A code has distance 5 if any two different codewords are at distance at least 5. It has minimum distance 5 if the minimum distance between two different codewords is 5. – Yuval Filmus Dec 6 '20 at 14:58

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