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 t₁ symmetric errors, up to t₂ unidirectional errors, and up to t ₃ asymmetric errors, as well as detecting from t₁+1 up to d₁ symmetric errors that are not of the unidirectional type, from t₂+1 up to d₂ unidirectional errors that are not of the asymmetric type, and from t₃+1 up to d₃ 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