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Undetected error probabilities of codes for single-error correction and error detection

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1 Author(s)
Lin, M.-C. ; Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan

It is shown that the probabilities of undetected errors for maximum-length codes are upper bounded by (n+1).2-(n-k), if the codes are used for correcting every single error and detecting other errors over a binary symmetric channel of which the transition probability is less than 1/2. Moreover, it is shown that binary linear codes with poor distance property do not satisfy the aforementioned bound.

Published in:

Electronics Letters  (Volume:27 ,  Issue: 24 )