ABSTRACT
Transmitter and receiver agree on the code to be used. Only codewords will be sent. If only one error occurs in the channel, then the received word will be in a ball of radius 1 around a codeword (in the Hamming metric). Assume the code has been chosen such that any two codewords are at distance at least 3. Then the balls of radius 1 do not overlap: if a bitstring has distance 1 from some codeword, then it has a larger distance from any other codeword. In other words, the receiver will decode any vector at distance = 1 from some codeword as that codeword. The notion of a binary code is too narrow, although it is most frequently used in information transmission. However, commercial telegraphy codes also took the reliability of message transmission into consideration.
