Undetected error probabilities of binary primitive BCH codes for both error correction and detection

In this paper, we investigate the undetected error probabilities for bounded-distance decoding of binary primitive BCH codes when they are used for both error correction and detection on a binary symmetric channel. We show that the undetected error probability of binary linear codes can be quite simplified and quantified if weight distribution of the code is binomial-like. We obtain bounds on the undetected error probability of binary primitive BCH codes by applying the result to the code and show that bounds are quantified by the deviation factor of true weight distribution from the binomial-like weight distribution.