Banca de DEFESA: ANDRE LUIS DOS SANTOS DUARTE DA SILVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : ANDRE LUIS DOS SANTOS DUARTE DA SILVA
DATA : 05/07/2021
HORA: 16:00
LOCAL: Por participação remota
TÍTULO:
PÁGINAS: 88
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
SUBÁREA: Álgebra
RESUMO:

 

In two hundred years many innovations in communication have helped people all
over the globe to connect. However, we still deal with the fundamental problem of
communication, reproducing at one point either exactly or approximately a message
send from another point. From this problem, new branches of mathematics were created,
such as Coding Theory and Information Theory.
In the first part of this thesis, we study "nilpotent codes" and approach the problem of
permutation equivalence between codes. In addition, we give conditions for monomial
equivalence between codes in a group algebra; in particular to cyclic codes. In the
case of minimal nilpotent codes a sufficient codition is given for being permutation
equivalent to abelian codes.
The second part is devoted to present a different method of computing the number of
simple components of a twisted group algebra. In addition, we compute the centrally
primitive idempotents of the twisted group algebras of a cyclic group and in the last
part we provide an example of idempotents in twisted group algebras.

MEMBROS DA BANCA:
Presidente - Interno ao Programa - 523.950.908-59 - FRANCISCO CESAR POLCINO MILIES - USP
Membro Titular - Examinador(a) Interno ao Programa - 1574072 - EDSON RYOJI OKAMOTO IWAKI
Membro Titular - Examinador(a) Externo à Instituição - ROBSON RICARDO DE ARAÚJO - IFSP
Membro Titular - Examinador(a) Externo à Instituição - ANDRE LUIZ MARTINS PEREIRA - UFRRJ
Membro Titular - Examinador(a) Externo à Instituição - RAUL ANTONIO FERRAZ - USP
Membro Suplente - Examinador(a) Interno ao Programa - 2278439 - NAZAR ARAKELIAN