Let C be an error-correcting code consisting of N codewords in which each codeword consists of n letters taken from an alphabet A of length q, and every two distinct codewords differ in at least d = 2e places. Then C is said to be nearly perfect if, for every possible word w_0 of length n with letters in A, there is a codeword w in C in which at most e letters of w differ from the corresponding letters of w_0. The codeword w is unique if it differs from w_0 in fewer than e places and there is at most one other codeword differing from w_0 in e places if w differs from w_0 in e places.

error-correcting code | Golay code | Hamming code | perfect code