Hamming codes

In this section, we present a commonly used linear error-correcting code which corrects exactly one error. In addition, it is the ``shortest'' code (linear or not) to do so. It was discovered by Hamming in the 1940's, in the days when an computer error would crash the computer and force the programmer to retype his punch cards. Out of frustration, he tried to design a system whereby the computer could automatically correct certain errors.