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Abstract
In this thesis, we study the notion of codes from group ring encodings due to hurley in [12]. This notion generalizes the classical cyclic codes over a {uFB01}nite {uFB01}eld which have been proven by F. MacWilliams to be the same as the ideals in a polynomial ring over the same {uFB01}eld. A necessary and su{uFB03}cient condition for a group ring to be code - checkable is given, when the base ring is {uFB01}nite commutative semisimple ring, as a generalization of the characterization given by Jitman in the case of the {uFB01}nite {uFB01}elds. We also study the notion of group codes over {uFB01}nite {uFB01}elds. We show that the major characterization of group codes given by Bernal et al, is still valid when the alphabet is a ring with identity