Quasi-Cyclic Complementary Dual Code

LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized. Constructions of QCCD codes from codes over larger alphabets are given

Quasi-cyclic subcodes of cyclic codes

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the simplex code and duals of certain BCH codes. Our results are based on the trace representation of cyclic codes

Multidimensional quasi-cyclic and convolutional codes

We introduce multidimensional generalizations of quasi-cyclic codes and investigate their algebraic properties as well as their links to multidimensional convolutional codes. We call these generalized codes n-dimensional quasi-cyclic (QnDC) codes. We provide a concatenated structure for QnDC codes in the sense that they can be decomposed into shorter codes over extensions of their base eld. This structure allows us to prove that these codes are asymptotically good. Then, we extend the relation between quasi-cyclic and convolutional codes to multidimensional case. Lally has shown that the free distance of a convolutional code is lower bounded by the minimum distance of an associated quasi-cyclic code. We show that a QnDC code can be associated to a given nD convolutional code. Moreover, we prove that the relation between distances of convolutional and quasicyclic codes extend to a class of 1-generator 2D convolutional codes and the associated Q2DC codes. Along the way, an alternative new description of noncatastrophic polynomial encoders is given for 1-generator 1D convolutional codes and a su cient condition for noncatastrophic nD polynomial encoders is obtained for 1-generator nD convolutional codes

Quasi-Cyclic Codes

Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some asymptotic results, a few minimum distance bounds and further applications such as the trace representation and characterization of certain subfamilies of quasi-cyclic codes are elaborated. This survey will appear as a chapter in "A Concise Encyclopedia of Coding Theory" to be published by CRC Press.Comment: arXiv admin note: text overlap with arXiv:1906.0496

Improved Spectral Bound for Quasi-Cyclic Codes

Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the corresponding eigenspaces, we provide an improved spectral bound for quasi-cyclic codes. Numerical results verify that the improved bound outperforms the Jensen bound in almost all cases. Based on the improved bound, we propose a general construction of quasi-cyclic codes with excellent designed minimum distances. For the quasi-cyclic codes produced by this general construction, the improved spectral bound is always sharper than the Jensen bound

Spectral Bounds for Quasi-Twisted Codes

New lower bounds on the minimum distance of quasi-twisted codes over finite fields are proposed. They are based on spectral analysis and eigenvalues of polynomial matrices. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a manner similar to how the Roos and shift bounds extend the BCH and HT bounds for cyclic codes.Comment: Accepted ISIT 201

Akut romatizmal ateş immünopatogenezinde ACE, MCP-1 ve IL-6 gen polimorfiziminin önemi

Bu tezin, veri tabanı üzerinden yayınlanma izni bulunmamaktadır. Yayınlanma izni olmayan tezlerin basılı kopyalarına Üniversite kütüphaneniz aracılığıyla (TÜBESS üzerinden) erişebilirsiniz.8.0ZET Bu çalışmada; çocukluk yaş grubunda, halen tam olarak aydınlatılamamış akut romatizmal ateş immünopatogenezinde meydana çıkan enflamasyonla ilgili değişikliklerin, ACE,MCP-1 ve IL-6 genotip alt gruplarını ve bu genotiplerdeki polimorfizim ile ilişkisinin olup olmadığının araştırılması ve elde edilen veriler doğrultusunda hastaların izlemine katkıda bulunmasını sağlamak amaçlanmıştır. Çalışmanın en önemli özelliği bugüne dek literatürde yayınlanmış olan çalışmalar içinde, çocukluk yaş grubu akut romatizmal ateş olgularında ilk kez araştırılmış olmasıdır. Çalışma, EÜTF Çocuk Sağlığı ve Hastalıkları Anabilim Dalı Pediatrik Kardiyoloji Bilim Dalında yatarak izlenen yaş ortalaması 10,98±2,9 olan 23 artrit ve 43 kardit tanılı ARA olguları ile,yaş ortalaması 11,85±2,2 olan ve her olgu için sistemik muayeneleri yapılıp kardiyak yönden patolojisi olmadığı belirlenen 66 kontrol olgusuna uygulandı. Çalışmaya dahil edilen olguların tümünde tedavi öncesi ve sonrası ASO,HB,HTC,SED,BK,CRP,EKG gibi laboratuar tetkikleri yapıldıktan sonra, Doppler ekokardiografik inceleme yapıldı. Hasta ve çalışma grubunda MCP-1,ACE ve IL-6 genotipleri ve bunlarda izlenen polimorfizm saptandı. Sonuçlar değerlendirilirken gerek artrit ve kardit olguları arasında, gerekse kontrol grupları arasında MCP-1.ACE ve IL-6 genotip sayı ve allel dağılımı araştırıldı. Çalışma sonucunda;hasta grubunda tedavi öncesi ve sonrası ASO,HB,SED,HTC,BK,CRP değerlerinde istatistiksel olarak anlamlılık saptandı. (p0. 01 ).Yine karditli olguların kardiyak değerlendirmesinde tedavi öncesi ve sonrası arasında anlamlılık saptandı. (p0. 01 )Hasta grubunda ACE homozigot DD,MCP-1 AA allel sıklığı fazla izlenmekle beraber kontrol grubuna göre anlamlı bulunmadı. (p>0. 05) Ancak IL-6 genotip dağılımı; kontrol grubuna göre istatistiksel olarak anlamlı bulundu. (p0.01) Fakat bu gruplarda hasta sayısının az olması nedeni ile artrit ve karditli olgular arasında genotip ve polimorfizm açısından istatistiksel olarak anlamlı fark saptanmadı. (p>0. 05) 78Sonuç olarak ;ARA immünopatogenezinde çok farklı etkenler olmakla beraber.gelişen inflamasyonun ACE.MCP-1 ve IL-6 ile ilişkili olarak da etkili olduğu sonucuna varıldı.Ancak; bu konuda kesitsel çalışmalar yerine sürekli ve geniş çalışmalar yapılması gerekmektedir. Bu konudaki sorunun en iyi cevabını artan çalışmalar verecekti

Multidimensional quasi-cyclic and convolutional codes

We introduce multidimensional analogues of quasi-cyclic (QC) codes and study their algebraic structure. We demonstrate a concatenated structure for multidimensional QC codes and use this to prove that this class of codes is asymptotically good. We also relate the new family of codes to convolutional codes. It is known that the minimum distance of QC codes provides a natural lower bound on the free distance of convolutional codes. We show that the same relation also holds between certain rank one 2-D convolutional codes and the related multidimensional QC codes. We provide examples, which show that our bound is sharp in some cases. We also present some optimal 2-D QC codes. Along the way, we provide a condition on the encoders of rank one convolutional codes, which are equivalent to noncatastrophicity for 1-D convolutional codes. In the nD case (n>1), our condition is sufficient for the noncatastrophicity of the encoder

New bounds on the minimum distance of cyclic codes

Two bounds on the minimum distance of cyclic codes are proposed. The first one generalizes the Roos bound by embedding the given cyclic code into a cyclic product code. The second bound also uses a second cyclic code, namely the non-zero-locator code, but is not directly related to cyclic product codes and it generalizes a special case of the Roos bound