The duals of MMD codes are proper for error detection

A linear code, when used for error detection on a symmetric channel, is said to be proper if the corresponding undetected error probability increases monotonically in ε, the symbol error probability of the channel. Such codes are generally considered to perform well in error detection. A number of well-known classes of linear codes are proper, e.g., the perfect codes, MDS codes, MacDonald´s codes, MMD codes, and some Near-MDS codes. The aim of this work is to show that also the duals of MMD codes are proper.