In the theory of block codes intended for error detection or error correction, the Hamming distance d(u, v) between two words u and v, of the same length, is equal to the number of symbol places in which the words differ from one another. If u and v are of finite length n then their Hamming distance is finite since

It can be called a distance since it is nonnegative, nil-reflexive, symmetric, and triangular:The Hamming distance is important in the theory of error-correcting codes and error-detecting codes: if, in a block code, the codewords are at a minimum Hamming distance d from one another, then

1. (a) if d is even, the code can detect d − 1 symbols in error and correct ½(d − 1) symbols in error;

2. (b) if d is odd, the code can detect d − 1 symbols in error and correct ½(d − 1) symbols in error.

See also coding bounds, coding theory, Hamming bound, Hamming space, perfect codes.