This work proposes a concatenated coding scheme which consists of inner polar codes and outer parity-check nodes aiming at increasing minimum distance. There have been a few studies on the concatenation of polar and parity-check codes, which are however heuristic approaches. This work instead proposes a systematic and deterministic algorithm based on a necessary condition to achieve an increased minimum distance. We demonstrate that the proposed coding scheme has a better error-rate performance as compared to those of competing codes such as polar-CRC codes, turbo codes and low-density parity-check (LDPC) codes at short lengths. In addition, it will be shown that codes with the proposed scheme can be efficiently decoded with a list successive cancellation (SC) decoder. The performance superiority of the proposed coding scheme will be confirmed via Monte-Carlo simulations.