Designs, Codes and Cryptography
Designs, Codes and Cryptography
Binomial Moments of the Distance Distribution and the Probabilityof Undetected Error
Designs, Codes and Cryptography
On the cyclic redundancy-check codes with 8-bit redundancy
Computer Communications
On the information function of an error-correcting code
IEEE Transactions on Information Theory
Almost-MDS and near-MDS codes for error detection
IEEE Transactions on Information Theory
A lower bound on the undetected error probability and strictly optimal codes
IEEE Transactions on Information Theory
Sufficient conditions for good and proper error-detecting codes
IEEE Transactions on Information Theory
A characterization of MMD codes
IEEE Transactions on Information Theory
Binomial moments of the distance distribution: bounds and applications
IEEE Transactions on Information Theory
A characterization of certain Griesmer codes: MMD codes in a more general sense
IEEE Transactions on Information Theory
The MMD codes are proper for error detection
IEEE Transactions on Information Theory
Discrete Applied Mathematics
Undetected error probability of q-ary constant weight codes
Designs, Codes and Cryptography
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Extended binomial moments of a linear code, introduced in this paper, are synonymously related to the code weight distribution and linearly to its binomial moments. In contrast to the latter, the extended binomial moments are monotone, which makes them appropriate for studying the undetected error probability. We establish some properties of the extended binomial moments and, based on this, derive new lower and upper bounds on the probability of undetected error. Also, we give a simplification of some previously obtained sufficient conditions for proper and good codes, stated in terms of the extended binomial moments.