Codes over finite modules / Noha Nouman Elgarem ; Supervised Nefertiti Megahed , Jay A. Wood , Mohamed Lamei
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TextLanguage: English Publication details: Cairo : Noha Nouman Elgarem , 2014Description: 131 P. ; 25cmOther title: - الأكواد على تشكيلات منتهية [Added title page title]
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Thesis
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قاعة الرسائل الجامعية - الدور الاول | المكتبة المركزبة الجديدة - جامعة القاهرة | Cai01.12.17.M.Sc.2014.No.C (Browse shelf(Opens below)) | Not for loan | 01010110065245000 | ||
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مخـــزن الرســائل الجـــامعية - البدروم | المكتبة المركزبة الجديدة - جامعة القاهرة | Cai01.12.17.M.Sc.2014.No.C (Browse shelf(Opens below)) | 65245.CD | Not for loan | 01020110065245000 |
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| Cai01.12.17.M.Sc.2014.Mu.N Numerical studies of di{uFB00}erential equations and their applications in financial mathematics / | Cai01.12.17.M.Sc.2014.Na.N Numerical studies for fractional- order delay di{uFB00}erential equations / | Cai01.12.17.M.Sc.2014.Na.N Numerical studies for fractional- order delay di{uFB00}erential equations / | Cai01.12.17.M.Sc.2014.No.C Codes over finite modules / | Cai01.12.17.M.Sc.2014.No.C Codes over finite modules / | Cai01.12.17.M.Sc.2014.Ta.N Numerical solutions of constrained optimal control problems for fractional order differential equations / | Cai01.12.17.M.Sc.2014.Ta.N Numerical solutions of constrained optimal control problems for fractional order differential equations / |
Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics
In this thesis, we revisit MacWilliams{u2019} classical results for codes over{uFB01}nite {uFB01}elds. The {uFB01}rst result is the MacWilliams identities. We study theseidentities in the classical setting and their generalizations to codes over {uFB01}nite rings and modules. The second result is the MacWilliams extension theorem, which states that two codes are isometric if and only if they aremonomially equivalent. MacWilliams proved this theorem in the 1960{u2019}s for codes over {uFB01}nite {uFB01}elds with respect to the Hamming weight. We study this theorem and how it was generalized to codes over {uFB01}nite rings and codes over {uFB01}nite modules, as well as to various weight functions. The main result of thethesis is proving a su{uFB03}cient condition for a module alphabet A to satisfy the extension property with respect to symmetrized weight compositions. Fi-nally, we introduce exotic isometries and give examples of this phenomenon
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