A survey on proper codes

The performance of a linear tt-error correcting code over a qq-ary symmetric memoryless channel with symbol error probability εε is characterized by the probability that a transmission error will remain undetected. This probability is a function of εε involving the code weight distribution and the weight distribution of the cosets of minimum weight at most tt. When the undetectable error probability is an increasing function of εε, the code is called tt-proper.The paper presents sufficient conditions for tt-properness and a list of codes known to be proper, many of which have been studied by these sufficient conditions. Special attention is paid to error detecting codes of interest in modern communication.