On the mis-correction due to any one extra bit error of Bose-Rao-Montgomery unidirectional error codes

By modifying the symmetric error correcting codes, Bose and Rao (1984) have obtained the unidirectional error-correcting (UEC) codes for shift register memories by using arithmetic redundancy check (ARC) in stead of cyclic redundancy check. Montgomery (see IEEE Trans. Comput., vol.40, p.1257, 1991) has proposed UEC code that correct any error pattern consisting of unidirectional errors confined to a single track. The UEC codes presented by Bose and Rao are a particular case of the codes by Montgomery. Although the latter is more efficient than the former, these two classes of code are constructed based on the same idea, and so the authors call these codes Bose Rao-Montgomery (BRM) codes. They consider the conditions under which such mis-corrections occur, and show that the row parity for each track is the suitable way of preventing from mis-corrections due to the single bit error in the other track