Covering radius and dual distance
Designs, Codes and Cryptography
Error control systems for digital communication and storage
Error control systems for digital communication and storage
Bounds on Spectra of Codes with Known Dual Distance
Designs, Codes and Cryptography
Estimates for the range of binomiality in codes' spectra
IEEE Transactions on Information Theory
Linear programming bounds for doubly-even self-dual codes
IEEE Transactions on Information Theory
On relations between covering radius and dual distance
IEEE Transactions on Information Theory
Estimates of the distance distribution of codes and designs
IEEE Transactions on Information Theory
An upper bound on the covering radius as a function of the dual distance
IEEE Transactions on Information Theory
Bounds on distance distributions in codes of known size
IEEE Transactions on Information Theory
Binomial and monotonic behavior of the probability of undetected error and the 2-r-bound
WSEAS TRANSACTIONS on COMMUNICATIONS
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Dual codes play an important role in the field of error detecting codes on a binary symmetric channel. Via the MacWilliams Identities they can be used to calculate the original code's weight distribution and its probability of undetected error. Moreover, knowledge of the minimum distance of the dual code provides insight in the properties of the weights of the code. In this paper firstly the order of growth of the dual distance of a CRC as a function of n is investigated, and a lower bound is given. Then, on one hand, this bound is used to derive an upper bound on the probability of undetected error of a CRC. On the other hand it is applied to some results about the range of binomiality and the covering radius of a CRC. Finally a new interpretation of Sidel'nikov's theorem on the cumulative distribution function of the weights of a code is given. In this way the conclusions may attribute a new meaning to some results about codes with known dual distance.