The MMD codes are proper for error detection

The undetected error probability of a linear code used to detect errors on a symmetric channel is a function of the symbol error probability ε of the channel and involves the weight distribution of the code. The code is proper, if the undetected error probability increases monotonously in ε. Proper codes are generally considered to perform well in error detection. We show in this correspondence that maximum minimum distance (MMD) codes are proper.