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Necessary and Sufficient Conditions on Block Codes Correcting/Detecting Errors of Various Types
September 1992 (vol. 41 no. 9)
pp. 1189-1193

Necessary and sufficient conditions are given for block codes to be capable of correcting up to t/sub 1/ symmetric errors, up to t/sub 2/ unidirectional errors, and up to t/sub 3/ asymmetric errors, as well as detecting from t/sub 1/+1 up to d/sub 1/ symmetric errors that are not of the unidirectional type, from t/sub 2/+1 up to d/sub 2/ unidirectional errors that are not of the asymmetric type, and from t/sub 3/+1 up to d/sub 3/ asymmetric errors. Many known conditions on block codes concerning error correction and/or detection appear as special cases of this general result. Further, some codes turn out to have stronger error correcting/detection capabilities than they were originally designed for.

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Index Terms:
necessary and sufficient conditions; error detection; block codes; symmetric errors; unidirectional errors; asymmetric errors; error correction; block codes; error correction codes; error detection codes.
Citation:
J.H. Weber, C. de Vroedt, D.E. Boekee, "Necessary and Sufficient Conditions on Block Codes Correcting/Detecting Errors of Various Types," IEEE Transactions on Computers, vol. 41, no. 9, pp. 1189-1193, Sept. 1992, doi:10.1109/12.165401
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