Why are Hamming codes the best 1-error-correcting codes? I need references. I know that hamming codes are the best 1-error-correcting codes but I want to know why they are best?
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1$\begingroup$ What is your source of that statement? Where have you looked and what have you tried towards showing optimality yourself? $\endgroup$– RaphaelDec 18, 2014 at 15:35
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The Hamming codes are optimal in the sense that among all codes with the same block length and minimal distance, they contain the most number of codewords. We know this because Hamming codes are perfect codes: their number of codewords matches the Hamming bound, which is an upper bound on the number of codewords in a code with given block length and minimal distance.
answered Dec 18, 2014 at 16:46