By injecting faults, active physical attacks pose serious threats to cryptographic hardware where Concurrent Error Detection (CED) schemes are promising countermeasures. They are usually based on an Error-Detecting Code (EDC) which enables detecting certain injected faults depending on the specification of the underlying code. Here, we propose a methodology to enable correct, practical, and robust implementation of code-based CEDs. We show that straightforward hardware implementations of given code-based CEDs can suffer from severe vulnerabilities, not providing the desired protection level. In particular, propagation of faults into combinatorial logic is often ignored in security evaluation of these schemes. First, we formally define this detrimental effect and demonstrate its destructive impact. Second, we introduce an implementation strategy to limit the fault propagation effect. Third, in contrast to many other works where the fault coverage is the main focus, we present a detailed implementation strategy which can guarantee the detection of any fault covered by the underlying EDC. This holds for any time of the computation and any location in the circuit, both in data processing and control unit. In short, we provide practical guidelines how to construct efficient CED schemes with arbitrary EDCs to achieve the desired protection level. We practically evaluate the efficiency of our methodology by case studies covering different symmetric block ciphers and various linear EDCs.