On quadratic residue codes over finite commutative chain rings
Dissertant
Abd Allah, Inad Hasan al-Ghandur Hasan
Thesis advisor
Comitee Members
Ashur, Arwa Id
al-Nauuq, Fayiq Ramadan
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2014
English Abstract
-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.
Main Subjects
No. of Pages
90
Table of Contents
Table of contents.
Abstract.
Introduction.
Chapter One : Preliminaries.
Chapter Two : Cyclic codes over nite chain rings.
Chapter Three : Quadratic residue codes over the rings Z4, Z8.
Chapter Four : Quadratic residue codes over the rings F2 + uF2, F2 + uF2 + u2F2 and F2 + uF2 + ... + um,1F2.
Conclusion.
References.
American Psychological Association (APA)
Abd Allah, Inad Hasan al-Ghandur Hasan. (2014). On quadratic residue codes over finite commutative chain rings. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-532057
Modern Language Association (MLA)
Abd Allah, Inad Hasan al-Ghandur Hasan. On quadratic residue codes over finite commutative chain rings. (Master's theses Theses and Dissertations Master). Islamic University. (2014).
https://search.emarefa.net/detail/BIM-532057
American Medical Association (AMA)
Abd Allah, Inad Hasan al-Ghandur Hasan. (2014). On quadratic residue codes over finite commutative chain rings. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-532057
Language
English
Data Type
Arab Theses
Record ID
BIM-532057
