On the Enumeration and Generation of Nonweight Equivalent Rate \frac{1}{2} Convolutional Codes

• Authors: Jean Conan
• Venue: Designs, Codes and Cryptography
• Year: 1997

The weight equivalence of rate \frac{1}{2} binary convolutionalcodes and the problem of enumeration and generation of all nonweightequivalent codes is considered for a given memory order m.This is done during the generation process by first orderingthe encoders into classes such that it becomes easy to recognizethe weight equivalence as well as the catastrophic error propagationconditions. Subclasses of respectively self and nonself reciprocalas well as catastrophic and noncatastrophic encoders are introduced.The cardinal number of these classes and subsequently the numberof ’’nonweight equivalent‘‘ codes are then computed recursivelyas a function of m. Finally, since all the relationsamount to simple convolutions they are compactly representedby generating functions which are tabulated.