ACS'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Applied Computer Science - Volume 7
Binomial and monotonic behavior of the probability of undetected error and the 2-r-bound
WSEAS TRANSACTIONS on COMMUNICATIONS
WSEAS TRANSACTIONS on COMMUNICATIONS
Optimal hash functions for approximate matches on the n-cube
IEEE Transactions on Information Theory
The minimum distance of the dual of a CRC
CIMMACS'07 Proceedings of the 6th WSEAS international conference on Computational intelligence, man-machine systems and cybernetics
A new exponential separation between quantum and classical one-way communication complexity
Quantum Information & Computation
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We treat the problem of bounding components of the possible distance distributions of codes given the knowledge of their size and possibly minimum distance. Using the Beckner inequality from harmonic analysis, we derive upper bounds on distance distribution components which are sometimes better than earlier ones due to Ashikhmin, Barg, and Litsyn. We use an alternative approach to derive upper bounds on distance distributions in linear codes. As an application of the suggested estimates we get an upper bound on the undetected error probability for an arbitrary code of given size. We also use the new bounds to derive better upper estimates on the covering radius, as well as a lower bound on the error-probability threshold, as a function of the code's size and minimum distance.