We characterize the traceability properties of linear codes. It is well known that any code of length n and minimum distance d is a c-TA code if c 2¿<¿n/(n¿-¿d). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value Z C , with n¿-¿d¿=¿Z C ¿=¿c(n¿-¿d), such that any linear code is c-TA if c¿<¿n/Z C . We also prove that in many cases this condition is also necessary. These results are applied to cyclic and Reed-Solomon codes.