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?
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.