Linear recurring sequences and the path weight enumerator of a convolutional code

The theory of integer recurrence relations is applied to give a new algebraic algorithm SYN ENUM which computes the path weight enumerator of a convolutional code. This algorithm may therefore be used to obtain performance bounds for a maximum likelihood decoder of a convolutional code. The path weight enumerator of a well known (2, 1, 6) code is computed.