On even length codes over finite rings
Dissertant
Thesis advisor
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2010
English Abstract
Codes over finite rings have been studied in the early 1970.
A great deal of attention has been given to codes over finite rings from 1990, because of their new role in algebraic coding theory and their successful application. The key to describing the structure of cyclic codes over a ring R is to view cyclic codes as ideals in the polynomial ring R [x] / (xn-1) where n is the length of the code.
In previous studies, some authors determined the structure of cyclic codes over Z4 for arbitrary even length by finding the generator polynomial, the number of cyclic codes for a given length and the duals for these codes, and also determined the structure of negacyclic codes of even length over the ring Z2a and their dual codes. In this thesis, we introduce cyclic codes of an arbitrary length n over the rings F2 + uF2 with u2 = 0 mod 2 and F2 + uF2 + u2F2 with u3 = 0 mod 2.
Wend a set of generatorsfor these codes.
The rank and the dual of these codes are studied as well.
We will extend these results about the rings F2 + uF2 and F2 + uF2 + u2F2 to more general rings F2 + uF2 + u2F2 = ...
+ u k-1 F2 with uk = 0 mod 2. Finally we study the structure of (1 + u)- constacyclic codes of even length n over the ring F2 + uF2 with u2 = 0 mod 2.
Also we extend this study to the ring F2 + uF2 + u2F2 with u3 = 0 mod 2.
nite rings have been studied in the early 1970.
A great deal of attention has been given to codes over nite rings from 1990, because of their new role in algebraic coding theory and their successful application. The key to describing the structure of cyclic codes over a ring R is to view cyclic codes as ideals in the polynomial ring R[x] xn ? 1 , where n is the length of the code. In previous studies, some authors determined the structure of cyclic codes over Z4 for arbitrary even length by nding the generator polynomial, the number of cyclic codes for a given length and the duals for these codes, and also determined the structure of negacyclic codes of even length over the ring Z2a and their dual codes. In this thesis, we introduce cyclic codes of an arbitrary length n over the rings F2 + uF2 with u2 = 0 mod 2 and F2 + uF2 + u2F2 with u3 = 0 mod 2.
We nd a set of generators for these codes.
The rank and the dual of these codes are studied as well. We will extend these results about the rings F2+uF2 and F2+uF2+u2F2 to more general rings F2 + uF2 + u2F2 = : : : + uk?1F2 with uk = 0 mod 2. Finally we study the structure of (1 + u)?constacyclic codes of even length n over the ring F2 + uF2 with u2 = 0 mod 2.
Also we extend this study to the ring F2 + uF2 + u2F2 with u3 = 0 mod 2
Main Subjects
Topics
No. of Pages
99
Table of Contents
Abstract.
Contents.
Chapter 1 : Preliminaries.
Chapter 2 : Cyclic codes over Z4 of even length.
Chapter 3 : Negacyclic codes of even length over z2a.
Chapter 4 : Cyclic codes over the ring F2 + uF2 + u2F2 +…+ uk-1F2.
Chapter 5 : Constacyclic codes over the rings F2 + uF2 and F2 + uF2 + u2F2.
American Psychological Association (APA)
Hamudih, Muhammad Abd. (2010). On even length codes over finite rings. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-300277
Modern Language Association (MLA)
Hamudih, Muhammad Abd. On even length codes over finite rings. (Master's theses Theses and Dissertations Master). Islamic University. (2010).
https://search.emarefa.net/detail/BIM-300277
American Medical Association (AMA)
Hamudih, Muhammad Abd. (2010). On even length codes over finite rings. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-300277
Language
English
Data Type
Arab Theses
Record ID
BIM-300277
