On the information function of an error-correcting code
IEEE Transactions on Information Theory
Bounds on the weight distribution of cosets
IEEE Transactions on Information Theory - Part 2
A lower bound on the undetected error probability and strictly optimal codes
IEEE Transactions on Information Theory
Extended Binomial Moments of a Linear Code and the Undetected Error Probability
Problems of Information Transmission
Discrete Applied Mathematics
Undetected error probability of q-ary constant weight codes
Designs, Codes and Cryptography
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In [1] K. A. S. Abdel-Ghaffarderives a lower bound on the probability of undetected errorfor unrestricted codes. The proof relies implicitly on the binomialmoments of the distance distribution of the code. We use thefact that these moments count the size of subcodes of the codeto give a very simple proof of the bound in Abdel by showingthat it is essentially equivalent to the Singleton bound. Thisproof reveals connections of the probability of undetected errorto the rank generating function of the code and to related polynomials(Whitney function, Tutte polynomial, and higher weight enumerators).We also discuss some improvements of this bound. Finally, we analyze asymptotics. We show that an upper boundon the undetected error exponent that corresponds to the boundof Abdel improves known bounds on this function.