Understanding and calculation of hamming Code

Hamming code (Hamming Code) is an error correction code that can have multiple check bits and can detect and correct one-bit error code, so it is only used in environments with good channel characteristics, such as Ethernet, because if the channel characteristics are not good, the error is usually not one.

The basic idea of error detection and correction of hamming code is to divide the effective information into several groups according to a certain rule, each group arranges a check bit for parity test, and then generates multi-bit detection information, from which the specific error location is obtained. finally, the error bit is corrected by inverting the error bit (the original 1 becomes 0, the original 0 becomes 1).

According to the error correction principle of hamming code, the following conclusions are obtained:

M+k+1