• العربية
    • English
  • English 
    • العربية
    • English
  • Login
Home
Publisher PoliciesTerms of InterestHelp Videos
Submit Thesis
IntroductionIUGSpace Policies
JavaScript is disabled for your browser. Some features of this site may not work without it.
View Item 
  •   Home
  • Faculty of Science
  • PhD and MSc Theses- Faculty of Science
  • View Item
  •   Home
  • Faculty of Science
  • PhD and MSc Theses- Faculty of Science
  • View Item

Please use this identifier to cite or link to this item:

http://hdl.handle.net/20.500.12358/21360
TitleLinear Block Codes over the Non Chain Ring Fp+ vFp + v2Fp
Title in Arabicالتراميز الخطية الموحدة على الحلقة غير التسلسلية
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 this thesis we study the structure and properties of linear and cyclic codes over the ring R2 = F2 + vF2 + v2F2 where v3 = v, which is a semi-local not chain ring. That we first study the relationship between cyclic codes over F2 + vF2 + v2F2 and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring, and we obtain the unique idempotent generators for cyclic codes of odd length and we study the (1 + v + v2)-constacyclic codes over R2. We also extend the study to linear and cyclic codes over the ring Rp = Fp + vFp + v2Fp, where v3 = v and p is prime greater than 2 such that Rp is a semi-local not chain ring. We firstly give the generator matrix of linear codes and their dual codes over Rp. Then, we define a Gray map Ψ from Rpn to Fp3n, and obtain Gray images Ψ(C) from the generator matrix of linear codes C over the ring Rp and we investigate the structure of cyclic codes over the ring Rp and give generator polynomials of cyclic codes over this ring . Then we study constacyclic codes over Rp. That we characterize the polynomial generators of all constacyclic codes over Rp, and show that constacyclic codes over Rp of arbitrary length are principally generated and we also discuss dual codes of constacyclic codes over Rp. Finally we introduce and study quadratic residue codes over the ring Rp in terms of their idempotent generators. And we study the structure of these codes and observe that these codes share similar properties with quadratic residue codes over finite fields.

Authors
Satariah, Mariam Ibrahim
Supervisors
Al-Ashker, Mohammed
Typeرسالة ماجستير
Date2015
LanguageEnglish
Publisherالجامعة الإسلامية - غزة
Citation
License
Collections
  • PhD and MSc Theses- Faculty of Science [445]
Files in this item
file_1.pdf1.369Mb
Thumbnail

The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

Contact Us | Send Feedback
 

 

Browse

All of IUGSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsSupervisorsThis CollectionBy Issue DateAuthorsTitlesSubjectsSupervisors

My Account

LoginRegister

Statistics

View Usage Statistics

The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

Contact Us | Send Feedback