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Codes that can correct up to t symmetric errors and detect all unidirectional errors are studied. BOumlinck and van Tilborg gave a bound on the length of binary such codes. A generalization of this bound to arbitrary alphabet size is given. This generalized BOumlinck-van Tilborg bound, combined with constructions, is used to determine some optimal binary and ternary codes for correcting t symmetric errors and detecting all unidirectional errors.