On the MacWilliams identity for convolutional codes

Heide Gluesing-Luerssen, Gert Schneider

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code. A MacWilliams Identity Conjecture, stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code, will be formulated, and an explicit formula for the transformation will be stated. The formula 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 itself or its dual does not have Forney indices bigger than one. For the general case, the conjecture is backed up by many examples, and a weaker version will be established.

Original languageEnglish
Pages (from-to)1536-1550
Number of pages15
JournalIEEE Transactions on Information Theory
Volume54
Issue number4
DOIs
StatePublished - Apr 2008

Keywords

  • Controller canonical form
  • Convolutional codes
  • MacWilliams identity
  • Weight adjacency matrix
  • Weight distribution

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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