Author: Homayoun ShahriPublisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 318
Book Description
Minimum Distance Bounds and Decoding of Cyclic Codes
Author: Homayoun ShahriPublisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 318
Book Description
On the Minimum Distance Structure of Cyclic Codes and Decoding Beyond the BCH Bound
Author: Carlos Ricardo Peixoto HartmannPublisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 158
Book Description
Two related aspects of cyclic codes have been investigated. An attempt has been made to obtain a better understanding concerning their minimum distance, and to find decoding methods to decode beyond the BCH bound. A theory is presented which enables one to obtain better bounds for the minimum distance of a large number of nonprimitive BCH codes. The derivation of this new theory is based on the use of more than one set of consecutive roots of the generator polynomial. The new results are easily applicable since they are based, as the BCH bound, on the pattern of the roots of the generator polynomial. A general decoding method to decode beyond the BCH bound is outlined. In addition a decoding method to decode beyond the BCH bound codes with minimum distance greater than the BCH bound and with multiple sets of consecutive roots is introduced. (Author).
On the Minimum Distance Structure of Cyclic Codes and Decoding Beyond Thebch Bound
Author: Error-Correction Coding and Decoding
Author: Martin TomlinsonPublisher: Springer
ISBN: 3319511033
Category : Technology & Engineering
Languages : en
Pages : 527
Book Description
This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th ese codes. Part IV deals with decoders designed to realize optimum performance. Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking. This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field. This book is open access under a CC BY 4.0 license.
On Minimum Distance Determination and Error-and-erasure Decoding of Cyclic Codes
Author: Hyun LeePublisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 222
Book Description
Minimum Distance and Decoding Algorithm for Cyclic Codes
Author: Anchung ChangExhaustive Search for the Best Cyclic (20,8) Code
Author: L. R. EspelandPublisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 36
Book Description
An exhaustive computer search for the best, simply implemented, cyclic (20, 8) codes was carried out, and the procedures and results are reported here. Some forty almost equally good (20, 8) codes are identified, but, alas, none of them appear to be better than the familiar (15, 5) Bose-Chaudhuri-Hocquenghem code.
Coding Theory, Cryptography and Related Areas
Author: Johannes BuchmannPublisher: Springer Science & Business Media
ISBN: 9783540662488
Category : Computers
Languages : en
Pages : 276
Book Description
A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects. The book will be useful to students, researchers, professionals, and tutors interested in this area of research.
Introduction to Coding Theory
Author: J. H. van LintPublisher: Springer Science & Business Media
ISBN: 3662079984
Category : Mathematics
Languages : en
Pages : 181
Book Description
Coding theory is still a young subject. One can safely say that it was born in 1948. It is not surprising that it has not yet become a fixed topic in the curriculum of most universities. On the other hand, it is obvious that discrete mathematics is rapidly growing in importance. The growing need for mathe maticians and computer scientists in industry will lead to an increase in courses offered in the area of discrete mathematics. One of the most suitable and fascinating is, indeed, coding theory. So, it is not surprising that one more book on this subject now appears. However, a little more justification of the book are necessary. A few years ago it was and a little more history remarked at a meeting on coding theory that there was no book available an introductory course on coding theory (mainly which could be used for for mathematicians but also for students in engineering or computer science). The best known textbooks were either too old, too big, too technical, too much for specialists, etc. The final remark was that my Springer Lecture Notes (# 201) were slightly obsolete and out of print. Without realizing what I was getting into I announced that the statement was not true and proved this by showing several participants the book Inleiding in de Coderingstheorie, a little book based on the syllabus of a course given at the Mathematical Centre in Amsterdam in 1975 (M. C. Syllabus 31).
Error-Correcting Linear Codes
Author: Anton BettenPublisher: Springer Science & Business Media
ISBN: 3540317031
Category : Mathematics
Languages : en
Pages : 819
Book Description
This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.