A survey on proper codes

Authors:
R. Dodunekova;S. M. Dodunekov;E. Nikolova
Affiliations:
Mathematical Sciences, Chalmers University of Technology and Göteborg University, 412 96 Göteborg, Sweden;Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G. Bonchev Str.1113, Sofia, Bulgaria;Computer Science, Bourgas Free University, 101 Aleksandrovska Str., 8000 Bourgas, Bulgaria
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

The performance of a linear t-error correcting code over a q-ary symmetric memoryless channel with symbol error probability @e is characterized by the probability that a transmission error will remain undetected. This probability is a function of @e 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 @e, 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.