Optimum Commutative Group Codes
Cristiano Torezzan, Jo\~ao E. Strapasson, Sueli I. R. Costa and, Rogerio M. Siqueira
TL;DR
This paper introduces a method to find optimal n-dimensional commutative group codes of a given size by analyzing lattice structures, reducing analysis complexity, and providing examples of optimal codes.
Contribution
It presents a novel approach using lattice theory and matrix factorizations to identify and classify optimal commutative group codes.
Findings
Reduced the number of non-isometric cases to analyze
Characterized isometric codes using matrix factorizations
Provided examples of optimal codes
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.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · graph theory and CDMA systems