Necessary and sufficient conditions on block codes correcting/detecting errors of various types

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.<>