Design of tch-type sequences for communications

• Author(s): Almeida, Alexandre M. C. Passos de
• Date: 2012
• Persistent ID: http://hdl.handle.net/10071/5889
• Origin: Repositório do ISCTE-IUL
• Subject(s): TIC - Tecnologias da informação e comunicação; Teoria dos números; Sistema de comunicação; Teoria dos ciclos
• Document Type: Doctoral Thesis
• Language: English

Description

Doctor in Information Science and Technology This thesis deals with the design of a class of cyclic codes inspired by TCH codewords. Since TCH codes are linked to finite fields the fundamental concepts and facts about abstract algebra, namely group theory and number theory, constitute the first part of the thesis. By exploring group geometric properties and identifying an equivalence between some operations on codes and the symmetries of the dihedral group we were able to simplify the generation of codewords thus saving on the necessary number of computations. Moreover, we also presented an algebraic method to obtain binary generalized TCH codewords of length N = 2k, k = 1,2, . . . , 16. By exploring Zech logarithm’s properties as well as a group theoretic isomorphism we developed a method that is both faster and less complex than what was proposed before. In addition, it is valid for all relevant cases relating the codeword length N and not only those resulting from N = pi