08-02-2013, 12:17 PM
LINEAR ALGEBRA APPLICATION TO CODING THEORY
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Introduction
Transmitted messages, like data from a satellite, are always subject to noise.
Therefore, to be able to encode a message in such a way that after noise scrambles it, it can be decoded to its original form.
This is done sometimes by repeating the message two or three times, something very common in human speech.
A code that detects errors in a scrambled message is called error detecting.
It can correct the error it is called error correcting.
Hamming code
In the 1950’s, R.H. Hamming introduced an interesting single error-correcting code that became known as the Hamming code.
Before we can examine the details of that technique, we need some background from linear algebra.