f service. Hamming designed a set of error Philippe Kurlapski at fr.wikisource (transferred from fr.wikisource): https://commons.wikimedia.org/wiki/ File%3AAccueil_scribe.png. Error Control Coding correction and detection codes known as Hamming codes in 1950. He was followed by other mathematicians who developed more powerful codes during the 1950s, codes which were soon used in digital telecommunication of information over noisy channels. A growing need for error-free communications especially with the emergence of the internet and electronic commerce, as well as the transmission power efficiencies error correction codes provide, has led to the development of stronger and more robust codes. These codes are now essential parts of all standards, from space to mobile to personal telecommunications systems. Furthermore, advances in computer processing power have made it possible to implement very complex codes to provide near-optimal performance as predicted by Shannon's theorem. Error control coding techniques have found applications in error-free storage as well as telecommunications, ensuring that holy text replicates, as well as other information, remain identical to the sources from which they are copied. In Chapter 5 we showed that digital telecommunications facilitate the removal of noise through regeneration of data. We further discussed that this is subject to correct detection of a received bit in the presence of noise and interference distortion; and that the rate of erro- neous detection, or bit error rate (BER) increases as the ratio of signal power to noise and interference power decreases. Given that there always exists a non-zero probability of erro- neous detection, several questions may be asked. Is it possible to know if any detection errors have occurred in a received data block? What BERs may be tolerated (analogous to how much noise may be tolerated e.g. in a voice call)? Is it possible to reduce detection errors by correction? In general, communications errors occur frequently. In everyday con