Codes over group rings /
الأكواد على الحلقات الزمرية
Noha Abdelghany ; Supervised Nefertiti Megahed , Tarek Sayed Ahmed
- Cairo : Noha Abdelghany , 2015
- 95 P. ; 25cm
Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics
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 nite eld which have been proven by F. MacWilliams to be the same as the ideals in a polynomial ring over the same eld. A necessary and sucient condition for a group ring to be code - checkable is given, when the base ring is nite commutative semisimple ring, as a generalization of the characterization given by Jitman in the case of the nite elds. We also study the notion of group codes over nite 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