Códigos convolucionais sobre Zpr [d]

  1. Rocha, Maria da Conceiçao Santos
Supervised by:
  1. María Raquel Rocha Pinto Director
  2. Diego Napp Avelli Co-director

Defence university: Universidade de Aveiro (UA)

Fecha de defensa: 22 November 2019

Committee:
  1. Mano Joao Filipe Colardelle da Luz Chair
  2. Rita Simões Committee member
  3. José Pedro Miranda Mourao Patrício Committee member
  4. Joan-Josep Climent Coloma Committee member

Type: Thesis

DIALNET lock_openOpen access editor

Abstract

The objects of study of this thesis are the free convolutional codes over the finite ring Z pr, where p is a prime and r is an integer greater than one, constituded by finite support sequences. The encoders of a free convolutional code are the image representations of the code. In this thesis we characterize the noncatastrophic encoder and we study the free distance and the column distances of a convolutional code that admits noncatastrophic encoders. Next, we consider the Input-State-Output (ISO) representation of these codes and we give an algoritm to obtain an ISO representation of a noncatastrophic code. We also obtain an ISO representation of minimal dimension for a particular class of these codes. Finally, we consider another type of encoder, a p-encoder, and we investigate the open problem stated by Kuijper and Pinto in 2009, about the existence of noncatastrophic p-encoders for a convolutional code over Z pr , constituted by left compact sequences. We have solved this problem for a particular class of these codes.