Hammingkoodiin

Hammingkoodiin, named after Richard Hamming, are a class of linear error-correcting codes. They are primarily used for detecting and correcting bit errors that can occur during data transmission or storage. The fundamental principle behind Hamming codes is the addition of redundant parity bits to the original data bits. These parity bits are calculated in such a way that they can pinpoint the location of a single-bit error.

The most common Hamming codes are Hamming(7,4) and Hamming(15,11). In Hamming(7,4), for instance, four data bits are encoded into seven bits, with three parity bits added. The positions of the parity bits are strategically chosen, typically at powers of two (1st, 2nd, 4th, 8th, etc., bit positions). Each parity bit is responsible for checking a specific subset of the data bits. When the data is received, the parity bits are recalculated and compared to the received parity bits. If there is a mismatch, the pattern of mismatches, known as the syndrome, directly indicates which bit is in error.

Hamming codes are efficient for correcting single-bit errors. However, they are generally not capable of correcting multiple-bit errors. If a double-bit error occurs, a Hamming code will often misinterpret it as a single-bit error and attempt to correct the wrong bit, thereby corrupting the data further. Despite this limitation, their simplicity and effectiveness in detecting and correcting single-bit errors make them a valuable tool in various applications, including computer memory (RAM), telecommunications, and satellite communication.