Bounds on the undetected error probabilities of linear codes for both error correction and detection

The author investigates the (n, k, d>or=2t+1) binary linear codes, which are used for correcting error patterns of weight at most t and detecting other error patterns over a binary symmetric channel. In particular, for t=1, it is shown that there exists one code whose probability of undetected errors is upper-bounded by (n+1) (2/sup n-k/-n)/sup -1/ when used on a binary symmetric channel with transition probability less than 2/n.<
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