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A simple derivation of the undetected error probabilities of complementary codes

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1 Author(s)
Abdel-Ghaffar, K.A.S. ; Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA

Recently, Fu, Klove, and Wei (2003) have shown that the undetected error probability of a binary code is related to that of its complement, and the undetected error probability of a constant-weight binary code is related to that of its complement relative to the set of all constant-weight vectors. We generalize these relations to cover the complements of any binary or nonbinary code relative to a distance-invariant code containing the first code. We prove the generalization using a much simpler argument than the published proofs of the special cases.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 5 )