ON ISOMETRIES FOR CONVOLUTIONAL CODES

被引：5
作者：
Gluesing-Luerssen, Heide [1 ]
机构：
[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2009年 / 3卷 / 02期
关键词：
Convolutional codes; strong isometries; state space realizations; weight adjacency matrix; monomial equivalence; MacWilliams Equivalence Theorem; EQUIVALENCE; TRELLIS; SPACES;
D O I：
10.3934/amc.2009.3.179
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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.
引用
收藏
页码：179 / 203
页数：25
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