On the undetected error probability for shortened Hamming codes

Shortened Hamming codes are widely used for error detection in data communications. In this paper, a method for computing the probability of an undetected error for these codes is presented. This method is then used to evaluate the error-detection performance of the shortened codes obtained from the two distance-four Hamming codes adopted by CCITT X.25 for error control for packet-switched networks. It is shown that shortening a code does affect its error-detection performance.