Quantum codes obtained from Gaussian and quaternion integers

Key Words: Quantum code, stabilizer code, nonbinary quantum code, linear code, cyclic code, additive codeThis thesis consist of four chapters. In the first chapter, some notations and some basic definitions and theorems of abstract algebra are given.In the second chapter, the fundamental elements needed to perform quantum computation and quantum information are described and many elementary operations which may be used to develop more sophisticated applications of quantum computation and quantum information are presented. Moreover, binary and nonbinary quantum error-correcting codes are explained.In the third chapter, the CSS codes are constructed from codes over Gaussian integers with respect to the Mannheim metric. Moreover, the set of the nice error bases over Gaussian integers is introduced.In the fourth chapter, the CSS codes are constructed via codes over quaternion integers with respect to the Lipschitz metric. Moreover, the set of the nice error bases over quaternion integers is introduced.