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May  2009, 3(2): 179-203. doi: 10.3934/amc.2009.3.179

On isometries for convolutional codes

Heide Gluesing-Luerssen 1,

1. 

Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027

Received  February 2009 Revised  April 2009 Published  May 2009

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.
Keywords: state space realizations, Convolutional codes, monomial equivalence, MacWilliams Equivalence Theorem., weight adjacency matrix, strong isometries.
Mathematics Subject Classification: Primary: 94B10, 94B05; Secondary: 93B15, 93B2.
Citation: Heide Gluesing-Luerssen. On isometries for convolutional codes. Advances in Mathematics of Communications, 2009, 3 (2) : 179-203. doi: 10.3934/amc.2009.3.179
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