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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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votes
Good codes in practice for correcting combination of errors and erasures
Your question is vague and open-ended. Here is a good book that you might start with (full text online):
http://www.inference.phy.cam.ac.uk/mackay/itila/