Abstract
The performance of a linear t -error correcting code over a q -ary symmetric memoryless channel with symbol error probability ε is characterized by the probability that a transmission error will remain undetected. This probability is a function of ε involving the code weight distribution and the weight distribution of the cosets of minimum weight at most t . When the undetectable error probability is an increasing function of ε , the code is called t -proper. The paper presents sufficient conditions for t -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.
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