A Matrix Ring Description for Cyclic Convolutional Codes
Information Theory
2007-08-13 v1 math.IT
Rings and Algebras
Abstract
In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe the algebraic parameters of the codes in a more accessible way. We show that the existence of such codes with given algebraic parameters can be reduced to the solvability of a modified rook problem. It is our strong belief that the rook problem is always solvable, and we present solutions in particular cases.
Cite
@article{arxiv.0708.1343,
title = {A Matrix Ring Description for Cyclic Convolutional Codes},
author = {Heide Gluesing-Luerssen and Fai-Lung Tsang},
journal= {arXiv preprint arXiv:0708.1343},
year = {2007}
}