These results are frustrating in that they offer little clue as to how the coding should be performed. Error detection coding is designed to permit the detection of errors. Once detected, the receiver may ask for a re-transmission of the erroneous bits, or it may simply inform the recipient that the transmission was corrupted. In a binary channel, error checking codes are called parity check codes.
Practical codes are normally block codes.
The rate of the code is the ratio , and the redundancy of the code is . Our ability to detect errors depends on the rate. A low rate has a high detection probability, but a high redundancy. The receiver will assign to the received codeword the preassigned codeword that minimises the Hamming distance between the two words. A very common code is the single parity check code .