TY  - BOOK
AU  - Noha Abdelghany
AU  - Nefertiti Megahed , 
AU  - Tarek Sayed Ahmed , 
TI  - Codes over group rings / 
PY  - 2015///
CY  - Cairo : 
PB  - Noha Abdelghany , 
KW  - Group codes
KW  - Group rings
KW  - Semisimple rings
N1  - Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics; Issued also as CD
N2  - 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
UR  - http://172.23.153.220/th.pdf
ER  -