We study a class of two-weight q-ary codes, considered by Baumert and McEliece, with regard to their properness or goodness in error detection. We prove for a large set of parameters that these codes are not good. For the remaining values of the parameters (which may or may not correspond to good codes) we determine if they are proper or not

The irreducible binary cyclic codes of even dimension, introduced by Delsarte and Goethals in 1970, constitute a parametric class with three parameters. We show that these codes and their duals are either proper or not good 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 /spl epsiv/, 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.

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

The performance of linear block codes over a finite field is investigated when they are used for pure error detection. Sufficient conditions for a code to be good or proper for error detection are derived.

The error detection capability of almost-MDS (AMDS) and nearly-MDS (NMDS) codes is studied. Necessary and sufficient conditions for the codes to be proper or good for error detection are given.