Hammingkóðun

Hammingkóðun, named after Richard Hamming, is a type of linear error-correcting code. It is widely used in data transmission and storage to detect and correct errors that may occur during these processes. The core principle of Hamming codes is the addition of redundant bits, called parity bits, to the original data. These parity bits are strategically placed and calculated based on the data bits.

When data is transmitted or stored, noise or physical defects can cause bits to flip, leading to errors. Hamming codes work by checking the parity of specific groups of bits. If the parity check fails, it indicates that an error has occurred. The specific pattern of parity check failures allows the receiver to pinpoint the exact location of the erroneous bit.

Once the error is detected and located, the Hamming code can also correct it by flipping the incorrect bit back to its original state. The number of parity bits added depends on the length of the original data. For instance, a Hamming code can correct single-bit errors. More advanced versions, like extended Hamming codes, can also detect double-bit errors. The efficiency of Hamming codes lies in their ability to achieve error correction with a minimal number of parity bits, making them a practical choice for many applications.