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On some properties of the undetected error probability of linear codes (Corresp.)

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3 Author(s)

A recent paper [1] discussed the 2^{-p} bound (where p = n- k ) for the probability of undetected error P(\epsilon) for an (n,k) block code used for error detection on a binary symmetric channel. This investigation is continued and extended and dual codes are studied. The dual and extension of a perfect code obey the 2^{-p} bound, but this is not necessarily true for arbitrary codes that obey the bound. Double-error-correcting BCH codes are shown to obey the bound. Finally the problem of constructing uniformly good codes is examined.

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Information Theory, IEEE Transactions on  (Volume:25 ,  Issue: 1 )