Códigos de hermite generalizados: algoritmos de decodificação de lista e aplicações.

Abstract

Algebraic-geometric (AG) codes are constructed from divisors of an algebraic curve, which can be supported in a single point or in several points, in this case, they are called multipoint. One-point AG codes have been extensively studied, as have various decoding algorithms and applications. The list decoding problem has been investigated this research for multipoint AG codes, as such algorithms present better performance even when desiring "single-word"lists, ie, compared to unique decoding algorithms, which are less flexible. In this sense, the main contribution of this thesis is a list decoding algorithm, which is based on the unique decoding algorithm proposed by Drake [1] for multipoint AG codes. In this research we investigated multipoint AG codes obtained from a generalization of the Hermitian curve, which allows the construction of code sequences with good parameters. Such codes are compared to Hermite codes and Reed-Solomon codes for communication system that use frequency hopping for code division multiple access. Generalized Hermitian codes allow to reach a larger number of users than using Reed-Solomon codes or Hermite codes without increasing the alphabet (finite body). In addition, comparative results are presented between these codes using packet error probability for packet radio network transmission systems, considering the AWGN channel and channels with partial band interference.