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Group Rings and applications in Coding theory.

Grant number: 12/23350-4
Support type:Scholarships in Brazil - Master
Effective date (Start): March 01, 2013
Effective date (End): January 31, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal researcher:Francisco Cesar Polcino Milies
Grantee:Tiago Henrique dos Reis
Home 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.

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