This paper's primary focus is on designing short parallel concatenated coding schemes and list-based decoding algorithms with low complexity. We aim to design a code with a relatively large minimum Hamming distance that can be efficiently decoded through list decoding. To achieve this, we introduce a novel parallel concatenated coding scheme, where the two constituent codes are linked by a full-rank matrix instead of the interleaver, which is commonly used in Turbo codes. The proposed code structures enable us to develop codes with significantly improved minimum Hamming distances. We also demonstrate that by utilizing a convolutional code as one of the constituent codes, we can effectively employ the parallel list Viterbi algorithm to generate a list of candidate codewords. Then, we select the candidate with the lowest Euclidean distance to the overall received signal. This allows us to use a highly complex constituent code, with potentially large minimum Hamming distance, as the second constituent code without increasing the decoding complexity. Simulation results validate the superior performance of these coding schemes compared to existing candidate coding schemes for short packet communications, particularly at very low rates.