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 = p
