Hammingetäisyydellä

Hammingetäisyydellä refers to the Hamming distance, a metric for comparing two strings of equal length. It is defined as the number of positions at which the corresponding symbols are different. For example, the Hamming distance between "karhu" and "karva" is 2, as the third and fourth letters are different. The Hamming distance is named after Richard Hamming.

This metric is widely used in coding theory and information theory, particularly in error detection and correction. When data is transmitted, errors can occur, causing some bits to flip. The Hamming distance between the original data and the received data can indicate the number of bit errors. If the Hamming distance is small, it suggests fewer errors.

In error correction codes, a minimum Hamming distance is established between valid codewords. If the Hamming distance between a received sequence and a valid codeword is below this minimum, it is considered to have an error. The greater the minimum Hamming distance, the more errors the code can detect and correct. For instance, a code with a minimum Hamming distance of 3 can detect up to 2 errors and correct 1 error.

The concept of Hamming distance is also applicable beyond binary strings. It can be used to compare strings of any alphabet, as long as they have the same length. However, its most common application remains in the realm of binary data.