Group Rings and applications in Coding theory.

• Grant number: 12/23350-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2013
• End date: January 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francisco Cesar Polcino Milies
• Grantee: Tiago Henrique dos Reis
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

A cyclic code, is a linear code such that if c = (c1, ..., cn) C then (cn, c1, ..., cn-1) C.If we denote by Cn the cyclic group of order n and by FqCn the group algebra of Cn over Fq, it is easy to see that every cyclic code can be accomplished as an ideal this algebra. This view has the advantage of allowingusing the group structure to determine the parameters of a code.Recently, A. Sharma, G. K. Bakshi and M. Raka studied cyclic codes of length 2m and determineted their weight distribution. These calculations were made considering the codes from the viewpoint of quotients ring of polynomials. The main work for the candidate thesis will be to understand these calculations and translate these ideas into the context of group algebras, aiming its simplifications and application of these ideas to new situations.