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 TypeDr GradeEmail
هتون عبداللطيف شعيبShoaib, Hatoon AbdullatifResearcherDoctorate 

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