Title :
A simple derivation of the undetected error probabilities of complementary codes
Author :
Abdel-Ghaffar, Khaled A S
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA
fDate :
5/1/2004 12:00:00 AM
Abstract :
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.
Keywords :
binary codes; error detection; error statistics; complementary code; constant-weight binary code; constant-weight vector; distance-invariant code; error detection; nonbinary code; undetected error probability; Binary codes; Equations; Error probability; Linear code; Polynomials;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2004.826672