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 2*k*+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 2*k*, 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.

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

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, nice sophia antipolis university, coding,informatics, hamming, error_detection,error_correcting_codes