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The theory of error-correcting codes stems from Shannon's 1948 _A mathematical theory of communication_, and from Hamming's 1950 "Error detecting and error correcting codes".

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Can you cover the Boolean cube $\{0,1\}^n$ with $O(1)$ Hamming-balls each of radius $n/2-c\s...

(where c>0 and the balls need not be disjoint?) This is an embarrassingly simple question, yet somehow I couldn't find an answer (not even, "this is a well-known open problem") after spending some ti …
Scott Aaronson's user avatar