A complete MacWilliams theorem for convolutional codes

Ching-Yi Lai, Min Hsiu Hsieh, Francis Lu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


In this paper, we prove a MacWilliams identity for the weight adjacency matrices based on the constraint codes of a convolutional code (CC) and its dual. Our result improves upon a recent result by Gluesing-Luerssen and Schneider, where the requirement of a minimal encoder is assumed. We can also establish the MacWilliams identity for the input-parity weight adjacency matrices of a systematic CC and its dual. Most importantly, we show that a type of Hamming weight enumeration functions of all codewords of a CC can be derived from the weight adjacency matrix, which thus provides a connection between these two very different notions of weight enumeration functions in the convolutional code literature. Finally, the relations between various enumeration functions of a CC and its dual are summarized in a diagram. This explains why no MacWilliams identity exists for the free-distance enumerators.

Original languageEnglish
Title of host publication2014 IEEE Information Theory Workshop, ITW 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781479959990
StatePublished - 1 Dec 2014
Event2014 IEEE Information Theory Workshop, ITW 2014 - Hobart, Australia
Duration: 2 Nov 20145 Nov 2014

Publication series

Name2014 IEEE Information Theory Workshop, ITW 2014


Conference2014 IEEE Information Theory Workshop, ITW 2014


Dive into the research topics of 'A complete MacWilliams theorem for convolutional codes'. Together they form a unique fingerprint.

Cite this