# Hamming code

Hamming codes are used for digital signal processing and telecommunications. Hamming codes are generated according to certain rules. Hamming codes use multiple parity bits. A parity bit tells whether a group of bits is even or odd. In a hamming code, each bit of data is covered by several parity bits. This allows to detect errors, and in certain cases, to correct them as well. A hamming code uses redundancy. If there are three parity bits per code word, the code word must have a length of 7 (${\displaystyle 2^{k}-1}$, for k as the number of parity bits). This leaves 4 bits of user data per code word, in the example. Usually, this is written as (N,n), where the first number is the total length of a code word, and the second is the number of bits for user data. The example above is (7,4).