Concerning a bound on undetected error probability

Abstract

In the past, it has generally been assumed that the probability of undetected error for an (n,k) block code, used solely for error detection on a binary symmetric channel, is upper bounded by 2-(n-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.