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It is conjectured that quantum computers are able to solve certain problemsmore quickly than any deterministic or probabilistic computer. A quantumcomputer exploits the rules of quantum mechanics to speed up computations.However, it is a formidable task to build a quantum computer, since the quantummechanical systems storing the information unavoidably interact with theirenvironment. Therefore, one has to mitigate the resulting noise and decoherenceeffects to avoid computational errors.  In this work, I study various aspects of quantum error control codes -- thekey component of fault-tolerant quantum information processing. I present thefundamental theory and necessary background of quantum codes and construct manyfamilies of quantum block and convolutional codes over finite fields, inaddition to families of subsystem codes over symmetric and asymmetric channels.  Particularly, many families of quantum BCH, RS, duadic, and convolutionalcodes are constructed over finite fields. Families of subsystem codes and aclass of optimal MDS subsystem codes are derived over asymmetric and symmetricquantum channels. In addition, propagation rules and tables of upper bounds onsubsystem code parameters are established. Classes of quantum and classicalLDPC codes based on finite geometries and Latin squares are constructed.

On Quantum and Classical Error Control Codes: Constructions and Applications