Towards a MacWilliams identity for convolutional codes

Heide Gluesing-Luerssen; Gert Schneider

doi:10.1109/ISIT.2007.4557625

Towards a MacWilliams identity for convolutional codes

Heide Gluesing-Luerssen, Gert Schneider

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The weight adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code. We will formulate a MacWilliams Identity Conjecture stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code. An explicit formula for the transformation will be stated as well; it involves the MacWilliams matrix known from complete weight enumerators of block codes. The conjecture will be proven for the class of convolutional codes where either the code or its dual is a unit memory code. For the general case the conjecture is backed up by many examples, and a weaker version will be established.

Original language	English
Title of host publication	Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007
Pages	2691-2695
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2007.4557625
State	Published - 2007
Event	2007 IEEE International Symposium on Information Theory, ISIT 2007 - Nice, France Duration: Jun 24 2007 → Jun 29 2007

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8101

Conference

Conference	2007 IEEE International Symposium on Information Theory, ISIT 2007
Country/Territory	France
City	Nice
Period	6/24/07 → 6/29/07

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT.2007.4557625

Cite this

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title = "Towards a MacWilliams identity for convolutional codes",

abstract = "The weight adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code. We will formulate a MacWilliams Identity Conjecture stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code. An explicit formula for the transformation will be stated as well; it involves the MacWilliams matrix known from complete weight enumerators of block codes. The conjecture will be proven for the class of convolutional codes where either the code or its dual is a unit memory code. For the general case the conjecture is backed up by many examples, and a weaker version will be established.",

author = "Heide Gluesing-Luerssen and Gert Schneider",

year = "2007",

doi = "10.1109/ISIT.2007.4557625",

language = "English",

isbn = "1424414296",

series = "IEEE International Symposium on Information Theory - Proceedings",

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Gluesing-Luerssen, H & Schneider, G 2007, Towards a MacWilliams identity for convolutional codes. in Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007., 4557625, IEEE International Symposium on Information Theory - Proceedings, pp. 2691-2695, 2007 IEEE International Symposium on Information Theory, ISIT 2007, Nice, France, 6/24/07. https://doi.org/10.1109/ISIT.2007.4557625

Towards a MacWilliams identity for convolutional codes. / Gluesing-Luerssen, Heide; Schneider, Gert.
Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007. 2007. p. 2691-2695 4557625 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Towards a MacWilliams identity for convolutional codes

Abstract

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