Please use this identifier to cite or link to this item: http://hdl.handle.net/10603/572790
Full metadata record
DC FieldValueLanguage
dc.coverage.spatial
dc.date.accessioned2024-06-21T11:16:47Z-
dc.date.available2024-06-21T11:16:47Z-
dc.identifier.urihttp://hdl.handle.net/10603/572790-
dc.description.abstractIn this thesis, we define and study a new class of additive codes over finite fields, viz. multi-twisted (MT) additive codes, which is a generalization of constacyclic additive codes and an extension of MT (linear) codes introduced by Aydin and Haliloviand#263; [5]. We study their algebraic structures by writing a canonical form decomposition of these codes using the Chinese Remainder Theorem and provide an enumeration formula for these codes. With the help of their canonical form decomposition, we also provide a trace description for all MT additive codes over finite fields. We further apply probabilistic methods to study the asymptotic properties of the rates and relative Hamming distances of a special subclass of 1-generator MT additive codes. We show that there exists an asymptotically good infinite sequence of MT additive codes of length pand#8629;` and block length pand#8629; ! 1 over Fqt with rate v pand#8984;`t and relative Hamming distance at least , where ` 1 and t 2 are integers, q is a prime power, Fqt is the finite field of order qt , p is an odd prime satisfying gcd(p, q)=1, v = ordp(q) is the multiplicative order of q modulo p, and#8984; is the largest positive integer such that pand#8984; | (qv 1) and is a positive real number satisfying hqt () lt 1 1 `t, (here hqt (·) denotes the qt -ary entropy function). This shows that the family of MT additive codes over finite fields is asymptotically good. As special cases, we deduce that the families of constacyclic and cyclic additive codes over finite fields are asymptotically good. By placing ordinary, Hermitian and and#8676; trace bilinear forms, we study the dual codes of MT additive codes over finite fields and derive necessary and sufficient conditions under which an MT additive code is (i) self-orthogonal, (ii) self-dual and (iii) an additive code with complementary dual (or an ACD code). We also derive a necessary and sufficient condition for the existence of a self-dual MT additive code over a finite field and provide enumeration formulae for all self-orthogonal, self-dual and ACD MT additive codes ov
dc.format.extent278 p.
dc.languageEnglish
dc.relation
dc.rightsuniversity
dc.titleOn some special classes of additive codes over finite fields
dc.title.alternative
dc.creator.researcherSharma, Sandeep
dc.subject.keywordMathematics
dc.subject.keywordSocial Sciences
dc.subject.keywordSocial Sciences Mathematical Methods
dc.description.note
dc.contributor.guideSharma, Anuradha
dc.publisher.placeDelhi
dc.publisher.universityIndraprastha Institute of Information Technology, Delhi (IIIT-Delhi)
dc.publisher.institutionDepartment of Mathematics
dc.date.registered
dc.date.completed2024
dc.date.awarded2024
dc.format.dimensions
dc.format.accompanyingmaterialNone
dc.source.universityUniversity
dc.type.degreePh.D.
Appears in Departments:Department of Mathematics

Files in This Item:
File Description SizeFormat 
01_title.pdfAttached File50.22 kBAdobe PDFView/Open
02_prelim pages.pdf669.53 kBAdobe PDFView/Open
03_content.pdf385.4 kBAdobe PDFView/Open
04_abstract.pdf338.88 kBAdobe PDFView/Open
05_chapter 1.pdf606.55 kBAdobe PDFView/Open
06_chapter 2.pdf885.51 kBAdobe PDFView/Open
07_chapter 3.pdf1.01 MBAdobe PDFView/Open
08_chapter 4.pdf880.64 kBAdobe PDFView/Open
09_chapter 5.pdf1.46 MBAdobe PDFView/Open
10_chapter 6.pdf1.22 MBAdobe PDFView/Open
11_chapter 7.pdf1.21 MBAdobe PDFView/Open
12_chapter 8.pdf1.61 MBAdobe PDFView/Open
13_annexures.pdf431.34 kBAdobe PDFView/Open
80_recommendation.pdf461.33 kBAdobe PDFView/Open


Items in Shodhganga are licensed under Creative Commons Licence Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0).

Altmetric Badge: