On isometries for convolutional codes

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5 Scopus citations


In this paper we will discuss isometries and strong isometries for convolutional codes. Isometries are weight-preserving module isomorphisms whereas strong isometries are, in addition, degree-preserving. Special cases of these maps are certain types of monomial transformations. We will show a form of MacWilliams Equivalence Theorem, that is, each isometry between convolutional codes is given by a monomial transformation. Examples show that strong isometries cannot be characterized this way, but special attention paid to the weight adjacency matrices allows for further descriptions. Various distance parameters appearing in the literature on convolutional codes will be discussed as well.

Original languageEnglish
Pages (from-to)179-203
Number of pages25
JournalAdvances in Mathematics of Communications
Issue number2
StatePublished - May 2009


  • Convolutional codes
  • MacWilliams equivalence theorem
  • Monomial equivalence
  • State space realizations
  • Strong isometries
  • Weight adjacency matrix

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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