Structural analysis of convolutional codes via dual codes

A linear correspondence is developed between the states of a rate- k/n convolutional encoder G and the states of a corresponding syndrome former HT, where H is an encoder of the code dual to the code generated by G. This correspondence is used to find an expression for the number of all-zero paths of length in the code trellis; the answer depends only on the constraint lengths of the dual code. A partial answer to the resynchronization problem also falls out of this development.