On the weight distribution of convolutional codes

Heide Gluesing-Luerssen

doi:10.1016/j.laa.2005.06.023

On the weight distribution of convolutional codes

Heide Gluesing-Luerssen

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Detailed information about the weight distribution of a convolutional code is given by the adjacency matrix of the state diagram associated with a minimal realization of the code. We will show that this matrix is an invariant of the code. Moreover, it will be proven that codes with the same adjacency matrix have the same dimension and the same Forney indices and finally that for one-dimensional binary convolutional codes the adjacency matrix determines the code uniquely up to monomial equivalence.

Original language	English
Pages (from-to)	298-326
Number of pages	29
Journal	Linear Algebra and Its Applications
Volume	408
Issue number	1-3
DOIs	https://doi.org/10.1016/j.laa.2005.06.023
State	Published - Oct 1 2005

Keywords

Controller canonical form
Convolutional coding theory
MacWilliams duality
Monomial equivalence
Weight distribution

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2005.06.023

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AB - Detailed information about the weight distribution of a convolutional code is given by the adjacency matrix of the state diagram associated with a minimal realization of the code. We will show that this matrix is an invariant of the code. Moreover, it will be proven that codes with the same adjacency matrix have the same dimension and the same Forney indices and finally that for one-dimensional binary convolutional codes the adjacency matrix determines the code uniquely up to monomial equivalence.

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KW - Convolutional coding theory

KW - MacWilliams duality

KW - Monomial equivalence

KW - Weight distribution

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On the weight distribution of convolutional codes

Abstract

Keywords

ASJC Scopus subject areas

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