What does the Hamming distance measure in the context of information theory and coding?

The Hamming distance is a measure used in information theory to quantify the difference between two strings of equal length. Specifically, it counts the number of positions at which the corresponding bits or characters in the two strings are different. For example, the Hamming distance between the binary strings 1010101 and 1001001 is 3, as they differ in three positions. This metric is particularly useful in various fields such as error detection and correction, where it helps determine how many bit changes are needed to convert one codeword into another. In coding theory, the Hamming distance between codewords can be used to assess the error-detecting and error-correcting capabilities of a code. A higher Hamming distance implies a better ability to detect and correct errors in data transmission or storage.