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