An upper bound on the average probability of undetected error for the ensemble of binary expanded generalized reed-Solomon codes

摘要

In this paper, we can get an upper bound on the average probability of undetected error for the ensemble of binary expanded generalized Reed-Solomon codes and simultaneously give a simple proof to show that the asymptotic distance ration for the ensemble of these codes meets the Varsharmov-Gilbert bound because this bound asymptotically meet that for the ensemble of all binary systematic block codes. Although it has been shown that most of these binary codes are asymptotically good by using an explicit average weight enumerator for the ensemble of these codes, the method in this paper is much simpler than one.