ABSTRACT
The most important measure of error detection is the Hamming distance. This defines the number of changes in the transmitted bits that are required in order for a code word to be received as another code word. The more bits that are added, the greater the Hamming distance can be, and the objective of a good error detecting code is to be able to maximize the minimum Hamming distance between codes. For example a code which has a minimum Hamming distance of 1 cannot be used to detect errors, as a single error in a specific bit in one or more code words will cause the received code word to be received as a valid code word. A minimum Hamming distance of 2 will allow one error to be corrected. In general, a code C can detect up to N errors for any code word if d(C) is greater than or equal to N + 1 (i.e. d(C)≥ N + 1). For this it can be shown that:
