The mathematics of finite fields and sequences seems to be a long way from everyday life, but it happens in the background every time we use a computer and without it, an explanation of modern error correction cannot be given.
Here we look at one of the first practical error-correcting codes to find wide usage. Richard Hamming worked with early computers and became frustrated when errors made them crash. The rest is history.
Errors are handled in real channels by a combination of techniques and it is the overall result that matters. This means that different media and channels can have completely different approaches to the problem, yet still deliver reliable data.
In the data recording or transmission fields, any time a recovered bit is not the same as what was supplied to the channel, there has been an error. Different types of data have different tolerances to error. Any time the error rate is in excess of the tolerance, we need