Modules with non-cyclic socle and the extension property /
Ali Assem Abdalqader Mahmoud
Modules with non-cyclic socle and the extension property / التشكيلات ذات القواعد غير الدائرية وخاصية الامتداد Ali Assem Abdalqader Mahmoud ; Supervised Nefertiti Megahed , Tarek Sayed Ahmad - Cairo : Ali Assem Abdalqader Mahmoud , 2016 - 97 P. ; 25cm
Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics
In 2009, J. Wood [43] proved that Frobenius bimodules have the extension property for symmetrized weight compositions. More generally, in [11], it is shown that having a cyclic socle is sufcient for satisfying the property, while the necessity remained an open question. Here, landing in Midway, a partial converse is proved. For a signicant class of nite module alphabets, the cyclic socle is shown necessary to satisfy the ex- tension property. The idea is bridging to the case of Hamming weight through a new weight function
Extension property Frobenius rings Linear codes
Modules with non-cyclic socle and the extension property / التشكيلات ذات القواعد غير الدائرية وخاصية الامتداد Ali Assem Abdalqader Mahmoud ; Supervised Nefertiti Megahed , Tarek Sayed Ahmad - Cairo : Ali Assem Abdalqader Mahmoud , 2016 - 97 P. ; 25cm
Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics
In 2009, J. Wood [43] proved that Frobenius bimodules have the extension property for symmetrized weight compositions. More generally, in [11], it is shown that having a cyclic socle is sufcient for satisfying the property, while the necessity remained an open question. Here, landing in Midway, a partial converse is proved. For a signicant class of nite module alphabets, the cyclic socle is shown necessary to satisfy the ex- tension property. The idea is bridging to the case of Hamming weight through a new weight function
Extension property Frobenius rings Linear codes