On the Probability of Undetected Error for Overextended Reed–Solomon Codes

Undetected Error Probability for Quantum Codes

Abstract From last fourteen years the work on undetected error probability for quantum codes has been silent. The undetected error probability has been discussed by Ashikhmin [3] in which it was proved that the average probability of undetected error for a given code is essentially given by a function of its weight enumerators. In this paper, new upper bounds on undetected error probability for...

On the Undetected Error Probability for Shortened Hamming Codes

On the undetected error probability of linear block codes on channels with memory

In the first part of the correspondence we derive an upper bound on the undetected error probability of binary ( n , k ) block codes used on channels with memory described by Markov distributions. This bound is a generalization of the bound presented by Kasami et al. for the binary symmetric channel, and is given as an average value of some function of the composition of the state sequence of t...

Concerning a Bound on Undetected Error Probability

In the past, it has generally been assumed that the prohability of undetected error for an (n,k) block code, used solely for error detection on a binary symmetric channel, is upperbounded by 2-‘“-k’. In this correspondence, it is shown that Hamming codes do indeed obey this bound, but that the bound is violated by some more general codes. Examples of linear, cyclic, and Bose-Chaudhuri-Hocquengh...

On the Binomial Moments of Linear Codes and Undetected Error Probability

The binomial moments of a linear code are synonymously related to its weight distribution and appear naturally in studies involving the weight distribution of the code. In particular , the binomial moments have been used for establishing bounds on the undetected error probability and, though implicitly, for the study of good and proper codes. In this work we sharpen known bounds on the binomial...