This principle is as follows. Ce principe est le suivant. For two words of the same length of a (binary) code, one define their Hamming distance by the number of bits (places) where the first word is different from the second.
If all the words of a code have a Hamming distance of at least 2k+1 from each other, then a word containing at most k erroneous bits is ``correctible'', as one can replace it by the code word nearest to it. And if the Hamming distance is at least 2k, one can correct words containing at most k-1 errors, as well as detect words containing k errors.
This exercise will therefore give you a code as well as a coded message containing errors. And you should decode this message, correcting correctible errors.
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Description: decode a message containing errors by an error correcting code. interactive exercises, online calculators and plotters, mathematical recreation and games
Keywords: interactive mathematics, interactive math, server side interactivity, coding, Hamming distance, error correcting code, error correction