Structural analysis of convolutional codes via dual codes
G. David Forney · IEEE Transactions on Information Theory · 1973
A linear correspondence is developed between the states of a rate-k/nconvolutional encoderGand the states of a corresponding syndrome formerH^T, whereHis an encoder of the code dual to the code generated byG. This correspondence is used to find an expression for the number of all-zero paths of length\tauin 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.