Please use this identifier to cite or link to this item: https://doi.org/10.1109/TIT.2006.880063
Title: A lower bound on the probability of undetected error for binary constant weight codes
Authors: Xia, S.-T.
Fu, F.-W. 
Ling, S.
Keywords: Binary constant weight codes
Distance distribution
Error detection
Probability of undetected error
Steiner systems
t-designs
Issue Date: Sep-2006
Citation: Xia, S.-T., Fu, F.-W., Ling, S. (2006-09). A lower bound on the probability of undetected error for binary constant weight codes. IEEE Transactions on Information Theory 52 (9) : 4235-4243. ScholarBank@NUS Repository. https://doi.org/10.1109/TIT.2006.880063
Abstract: In this correspondence, we study the probability of undetected error for binary constant weight codes. First, we derive a new lower bound on the probability of undetected error for binary constant weight codes. Next, we show that this bound is tight if and only if the binary constant weight codes are generated from certain t-designs in combinatorial design theory. This means that these binary constant weight codes generated from certain t-designs are uniformly optimal for error detection. Along the way, we determine the distance distributions of such binary constant weight codes. In particular, it is shown that binary constant weight codes generated from Steiner systems are uniformly optimal for error detection. Thus, we prove a conjecture of Xia, Fu, Jiang, and Ling. Furthermore, the distance distribution of a binary constant weight code generated from a Steiner system is determined. Finally, we study the exponent of the probability of undetected error for binary constant weight codes. We derive some bounds on the exponent of the probability of undetected error for binary constant weight codes. These bounds enable us to extend the region in which the exponent of the probability of undetected error is exactly determined. © 2006 IEEE.
Source Title: IEEE Transactions on Information Theory
URI: http://scholarbank.nus.edu.sg/handle/10635/111311
ISSN: 00189448
DOI: 10.1109/TIT.2006.880063
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