A brief discussion of the role of coding theory in a communications system is followed by a description of convolutional codes and various distances measures. Two theorems and several corollaries concerning free distance are presented. The first theorem is essentially a correction of a counterexample to a conjecture relating free distance and column distance. The second demonstrates a necessary and sufficient condition for the free distance of a canonic systematic code to equal its order M'column distance. A corollary shows that the condition is a sufficient one for a nonsystematic code also. Two expressions for the probability of undetectable error of a specific code are presented. (Author)
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