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.
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$\begingroup$ 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. $\endgroup$Yuval Filmus– Yuval Filmus2020-12-06 14:58:56 +00:00Commented Dec 6, 2020 at 14:58
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1 Answer
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0000000000
1111100000
0000011111
1111111111
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$\begingroup$ Is there a general algorithm for this problem? Given number of code words and minimum distance, find a code of minimum required length. $\endgroup$alexei– alexei2023-04-13 02:00:17 +00:00Commented Apr 13, 2023 at 2:00
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$\begingroup$ You can always use exhaustive search. $\endgroup$Yuval Filmus– Yuval Filmus2023-04-13 16:33:29 +00:00Commented Apr 13, 2023 at 16:33