Optimum commutative group codes

Author(s)

Torezzan, Cristiano ^[1] ; Strapasson, Joao E. ^[1] ; Costa, Sueli I. R. ^[2] ; Siqueira, Rogerio M. ^[3]

Affiliation

^[1] Univ Estadual Campinas, Sch Appl Sci, BR-13083859 Sao Paulo - Brazil

^[2] Univ Estadual Campinas, Inst Math, BR-13083859 Sao Paulo - Brazil

^[3] Univ Sao Paulo, Sch Arts Sci & Humanities, Sao Paulo - Brazil

• Document type: Journal article
• Source: DESIGNS CODES AND CRYPTOGRAPHY; v. 74, n. 2, p. 379-394, FEB 2015.
• Web of Science Citations: 2

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. (AU)

• FAPESP's process: 05/58102-7 - Códigos corretores de erros gerados por grupos de simetrias
• Grantee: Cristiano Torezzan
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• FAPESP's process: 11/01096-6 - Discrete mathematics: lattices, codes and cryptography
• Grantee: João Eloir Strapasson
• Support Opportunities: Regular Research Grants
• FAPESP's process: 02/14072-9 - Códigos geometricamente uniformes em espaços de curvatura constante e em grafos regulares
• Grantee: Rogerio Monteiro de Siqueira
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 07/56052-8 - Teoria da informação e códigos
• Grantee: Sueli Irene Rodrigues Costa
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 07/00514-3 - Geometry and codes theory
• Grantee: João Eloir Strapasson
• Support Opportunities: Scholarships in Brazil - Post-Doctoral