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Codes over group rings / Noha Abdelghany ; Supervised Nefertiti Megahed , Tarek Sayed Ahmed

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Cairo : Noha Abdelghany , 2015Description: 95 P. ; 25cmOther title:
  • الأكواد على الحلقات الزمرية [Added title page title]
Subject(s): Online resources: Available additional physical forms:
  • Issued also as CD
Dissertation note: Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics Summary: 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
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Thesis Thesis قاعة الرسائل الجامعية - الدور الاول المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2015.No.C (Browse shelf(Opens below)) Not for loan 01010110068967000
CD - Rom CD - Rom مخـــزن الرســائل الجـــامعية - البدروم المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2015.No.C (Browse shelf(Opens below)) 68967.CD Not for loan 01020110068967000

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 {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

Issued also as CD

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