Main Page
Deanship
The Dean
Dean's Word
Curriculum Vitae
Contact the Dean
Vision and Mission
Organizational Structure
Vice- Deanship
Vice- Dean
KAU Graduate Studies
Research Services & Courses
Research Services Unit
Important Research for Society
Deanship's Services
FAQs
Research
Staff Directory
Files
Favorite Websites
Deanship Access Map
Graduate Studies Awards
Deanship's Staff
Staff Directory
Files
Researches
Contact us
عربي
English
About
Admission
Academic
Research and Innovations
University Life
E-Services
Search
Deanship of Graduate Studies
Document Details
Document Type
:
Thesis
Document Title
:
On Multi-negacirculant and Quasi-polycyclic Codes
الترميزات السالب دائرية المتعددة والشبه دائرية المتعددة
Subject
:
Faculty of Sciences
Document Language
:
Arabic
Abstract
:
Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. In this thesis, self-dual DN are shown to have a transitive automorphism group. Exact counting formulae are derived for DN codes. The special class of length a power of two is studied by means of Dickson polynomials, and is shown to contain families of codes with relative distances satisfying a modified Gilbert-Varshamov bound. This gives an alternative, and effective proof of the result of Chebyshev, that there are families of quasi-twisted codes above improving on the Gilbert-Varshamov bound. Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index 2 that are LCD are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, and for all indices t for a special case of the co-index by using their concatenated structure. Asymptotic existence results are derived for the special class of such codes that are one-generator and have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of LCD multinegacirculant codes with relative distance satisfying a modified Gilbert-Varshamov bound. We study complementary information set codes of length tn and dimension n of order t called t-CIS code for short. Quasi-cyclic and quasi-twisted t-CIS codes are enumerated by using their concatenated structure. Asymptotic existence results are derived for one-generator codes and have co-index n by Artin's conjecture for quasi-cyclic and in the special case for quasi-twisted. This shows that there are infinite families of long QC and QT t-CIS codes with relative distance satisfying a modified Gilbert-Varshamov bound for rate 1/t codes. Similar results are defined for the new and more general class of quasi-polycyclic codes introduced recently by Berger and Amrani.
Supervisor
:
Dr. Adel Naif Alahmadi
Thesis Type
:
Doctorate Thesis
Publishing Year
:
1438 AH
2017 AD
Added Date
:
Wednesday, May 31, 2017
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
هتون عبداللطيف شعيب
Shoaib, Hatoon Abdullatif
Researcher
Doctorate
Files
File Name
Type
Description
40822.pdf
pdf
Back To Researches Page