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Sep 29, 2016 at 14:51 vote accept Jairo Bochi
Sep 28, 2016 at 23:08 answer added John Machacek timeline score: 2
Sep 28, 2016 at 20:10 comment added Jairo Bochi This seems to be a good entry point in the theory: en.wikipedia.org/wiki/Hamming_bound It's seems clear that the short answers to my questions are "no"s.
Sep 28, 2016 at 19:56 comment added Jairo Bochi Thanks Adreas and Fedor. Now I see that d is called the Hamming distance.
Sep 28, 2016 at 19:49 comment added Fedor Petrov Already for $m=2$ this problem is famous: it is a central question in the coding theory, there are various estimates, and rarely exact values are known.
Sep 28, 2016 at 19:47 comment added Andreas Blass I'm afraid a good answer to this question would be an exposition of a large part of coding theory. Since I'm not qualified to write that, let me just refer to the Wikipedia article en.wikipedia.org/wiki/Coding_theory, in particular the section on channel coding.
Sep 28, 2016 at 19:13 history asked Jairo Bochi CC BY-SA 3.0