The free distance of (n, k, l) convolutional codes has some connection with the memory length, which depends on not only l but also on k. To efficiently obtain a large memory length, we have constructed a new class of (2k, k, l) convolutional codes by (2k, k) block codes and (2, 1, l) convolutional codes, and its encoder and generation function are also given in this paper. With the help of some matrix modules, we designed a single structure Viterbi decoder with a parallel capability, obtained a unified and efficient decoding model for (2k, k, l) convolutional codes, and then give a description of the decoding process in detail. By observing the survivor path memory in a matrix viewer, and testing the role of the max module, we implemented a simulation with (2k, k, l) convolutional codes. The results show that many of them are better than conventional (2, 1, l) convolutional codes.