Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile
Abstract
Superregular matrices are a class of lower triangular Toeplitz matrices that arise in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that no submatrix has a zero determinant unless it is trivially zero due to the lower triangular structure. In this paper, we discuss how superregular matrices may be used to construct codes having a maximum distance profile. We also introduce group actions that preserve the superregularity property and present an upper bound on the minimum size a finite field must have in order that a superregular matrix of a given size can exist over that field.
Cite
@article{arxiv.cs/0607089,
title = {Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile},
author = {R. Hutchinson and R. Smarandache and J. Trumpf},
journal= {arXiv preprint arXiv:cs/0607089},
year = {2007}
}
Comments
20 pages. Replaced on 19/7/2006, because bibtex files were not included in the original submission