Concerning a Bound on Undetected Error Probability

In the past, it has generally been assumed that the prohability of undetected error for an (n,k) block code, used solely for error detection on a binary symmetric channel, is upperbounded by 2-‘“-k’. In this correspondence, it is shown that Hamming codes do indeed obey this bound, but that the bound is violated by some more general codes. Examples of linear, cyclic, and Bose-Chaudhuri-Hocquenghem (BCH) codes which do not obey the bound are given.