Concerning a bound on undetected error probability
Kamal Gupta · International Journal of Statistics and Applied Mathematics · 2017
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.