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Separable error-correcting/detecting codes are developed that provide protection against combinations of both unidirectional and random errors. Specifically, codes are presented which can both: 1) correct (detect) some t random errors, and 2) detect any number of unidirectional errors which may also contain t or fewer random errors. Necessary and sufficient conditions for the existence of these codes are also developed. Decoding algorithms for these codes are presented, and implementations of the algorithms are also discussed.