On quadratic residue codes over finite commutative chain rings

مقدم أطروحة جامعية

Abd Allah, Inad Hasan al-Ghandur Hasan

مشرف أطروحة جامعية

al-Ashker, Muhammad Mahmud

أعضاء اللجنة

Ashur, Arwa Id
al-Nauuq, Fayiq Ramadan

الجامعة

الجامعة الإسلامية

الكلية

كلية العلوم

القسم الأكاديمي

قسم الرياضيات

دولة الجامعة

فلسطين (قطاع غزة)

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2014

الملخص الإنجليزي

-Codes over nite rings were initiated in the early 1970s, And they have received much attention after it was proved that important families of binary non-linear codes are images under a Gray map of linear codes over Z4.

In this thesis we consider a special families of cyclic codes namely Quadratic residue codes over nite chain rings F2 + uF2 with u2 = 0 and F2 + uF2 + u2F2 with u3 = 0.

We study these codes in term of their idempotent generators, and show that these codes have many good properties which are analogous in many respect to properties of Quadratic residue codes over nite elds, also, we study Quadratic residue codes over the ring Z2m, and then generalize this study to Quadratic residue codes over nite commutative chain ring Rm?1 = F2 + uF2 + : : : + um?1F2 with um = 0.

التخصصات الرئيسية

الرياضيات

عدد الصفحات

90

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-532057