G-Equivalence in Group Algebras and Minimal Abelian Codes

Author(s)

Ferraz, Raul Antonio ^[1] ; Guerreiro, Marines ^[2] ; Milies, Cesar Polcino ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05314970 Sao Paulo - Brazil

^[2] Univ Fed Vicosa, Dept Matemat, BR-36570000 Vicosa, MG - Brazil

• Document type: Journal article
• Source: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 60, n. 1, p. 252-260, JAN 2014.
• Web of Science Citations: 2

Abstract

Let G be a finite Abelian group and F a field such that char (F) does not divide vertical bar G vertical bar. Denote FG by the group algebra of G over F. A (semisimple) Abelian code is an ideal of FG. Two codes I-1 and I-2 of FG are G-equivalent if there exists an automorphism psi of G whose linear extension to FG maps I-1 onto I-2. In this paper, we give a necessary and sufficient condition for minimal Abelian codes to be G-equivalent and show how to correct some results in the literature. (AU)

• FAPESP's process: 09/52665-0 - Groups, rings and algebras: interactions and applications
• Grantee: Francisco Cesar Polcino Milies
• Support Opportunities: Research Projects - Thematic Grants