Optimum Commutative Group Codes
Information Theory
2013-03-26 v2 Group Theory
math.IT
Abstract
A method for finding an optimum -dimensional commutative group code of a given order is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric commutative group codes. Several examples of optimum commutative group codes are also presented.
Cite
@article{arxiv.1205.4067,
title = {Optimum Commutative Group Codes},
author = {Cristiano Torezzan and João E. Strapasson and Sueli I. R. Costa and Rogerio M. Siqueira},
journal= {arXiv preprint arXiv:1205.4067},
year = {2013}
}