Construction and Decoding of Codes on Finite Fields and Finite Geometries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Construction and Decoding of Codes on Finite Fields and Finite Geometries write by Li Zhang. This book was released on 2010. Construction and Decoding of Codes on Finite Fields and Finite Geometries available in PDF, EPUB and Kindle. In this doctoral dissertation, two constructions of binary low-density parity-check (LDPC) codes with quasi-cyclic (QC) structures are presented. A general construction of RC-constrained arrays of circulant permutation matrices is introduced, then two specific construction methods based on Latin squares and cyclic subgroups are presented. Array masking is also proposed to improve the waterfall-region performance of the QC-LDPC codes. Also, by analyzing the parity check matrices of these codes, combinatorial expressions for their ranks and dimensions are derived. Experimental results show that, with iterative decoding algorithms, the constructed codes perform very well over both the additive white Gaussian noise (AWGN) and the binary erasure channels (BEC). Also presented in this dissertation are constructions of QC-LDPC codes based on two special classes of balanced incomplete block designs (BIBDs) derived by Bose. Codes are constructed for both the AWGN channel and the binary burst erasure channel (BBEC). Experimental results show that the codes constructed perform well not only over these two types of channels but also over the BEC. Finally, a two stage iterative decoding is presented to decode a class of cyclic Euclidean geometry codes. By exploiting the inherent geometry structure of the codes and avoiding the degrading effect of short cycles, the proposed algorithm provides good decoding performance of the codes.
Geometries, Codes and Cryptography
Geometries, Codes and Cryptography - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometries, Codes and Cryptography write by G. Longo. This book was released on 2014-05-04. Geometries, Codes and Cryptography available in PDF, EPUB and Kindle. The general problem studied by information theory is the reliable transmission of information through unreliable channels. Channels can be unreliable either because they are disturbed by noise or because unauthorized receivers intercept the information transmitted. In the first case, the theory of error-control codes provides techniques for correcting at least part of the errors caused by noise. In the second case cryptography offers the most suitable methods for coping with the many problems linked with secrecy and authentication. Now, both error-control and cryptography schemes can be studied, to a large extent, by suitable geometric models, belonging to the important field of finite geometries. This book provides an update survey of the state of the art of finite geometries and their applications to channel coding against noise and deliberate tampering. The book is divided into two sections, "Geometries and Codes" and "Geometries and Cryptography". The first part covers such topics as Galois geometries, Steiner systems, Circle geometry and applications to algebraic coding theory. The second part deals with unconditional secrecy and authentication, geometric threshold schemes and applications of finite geometry to cryptography. This volume recommends itself to engineers dealing with communication problems, to mathematicians and to research workers in the fields of algebraic coding theory, cryptography and information theory.
Algebraic Geometry Codes: Advanced Chapters
Algebraic Geometry Codes: Advanced Chapters - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry Codes: Advanced Chapters write by Michael Tsfasman. This book was released on 2019-07-02. Algebraic Geometry Codes: Advanced Chapters available in PDF, EPUB and Kindle. Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to local_libraryBook Catalogseveral domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.
Algebraic-Geometric Codes
Algebraic-Geometric Codes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic-Geometric Codes write by M. Tsfasman. This book was released on 2013-12-01. Algebraic-Geometric Codes available in PDF, EPUB and Kindle. 'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d' etre of this series.
Introduction to Coding Theory and Algebraic Geometry
Introduction to Coding Theory and Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Coding Theory and Algebraic Geometry write by J. van Lint. This book was released on 1988-09-01. Introduction to Coding Theory and Algebraic Geometry available in PDF, EPUB and Kindle. These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course.
