In certain applications where the integrity of stored or transmitted data may be compromised by security breaches, or errors may arise due to other reasons, it is important to have some method to detect that errors have occurred that need to be fixed.

An analogy can be used to illustrate the problem. If we are not sure whether certain text received--that is supposed to be prose in contemporary English--is actually error-free, then it suffices to check whether any of the words in the received text are misspelled. If we find words that are not found in the dictionary, or else are spelled in a manner different from the dictionary, then we may infer that errors have occurred. Once such an error is detected, recovery may be attempted either by requesting the sender to supply a replacement for the missing or incorrect information, or else by trying...