A class of (12, 8) codes for correcting single errors and detecting double errors within a nibble

A class of (12, 8) codes is given that corrects all single errors, and detects all double errors in the three nibbles. It is shown that there exist three distinct solutions to this problem. One of these can be implemented with an LS636/7 chip. It is also shown that there do not exist any other codes except these three which correct all single errors and detect adjacent double errors confined to a nibble.<
>