Conventionally, the free distance is taken as the principle criterion for computing the error of convolutional and linear block codes. In other words, a larger free distance implies a better correction ability for the error correction codes. Distance spectrum is also an important factor for Maximum likelihood decoding. In this thesis, distance spectrum for different convolutional codes and CPM systems are investigated by us. Experiments results has demonstrate that a better correction ability of a shorter free distance does exist in some cases if they have a better distance spectrum. We also improve the fast algorithm for computing the distance spectrum developed by M. Cedervall and R. Johannesson. Their success is based upon the strategy of a traveling along the coding tree to find the distance spectrum. However, they need a new traveling for ever new distance computation. In contrast, we compute all the distance spectrum just in one travel by taking the advantage of the storing nodes of previous distance computation.

Error control coding is employed in modern communication systems to reliably transfer data through noisy channels. Convolutional codes are widely used for this purpose because they are easy to encode and decode and so have been employed in numerous communication systems. The focus of this thesis is a search for new and better ternary convolutional codes with large free distance so more errors can be detected and corrected. An algorithm is developed to obtain ternary convolutional codes (TCCs) with the best possible free distance. Tables are given of binary and ternary convolutional codes with the best free distance for rate 1/2 with encoder memory up to 14, rate 1/3 with encoder memory up to 9 and rate 1/4 with encoder memory up to 8. / Graduate