Some aspects of the construction and implementation of error-correcting linear codes

Some aspects of the construction and implementation of error-correcting linear codes PDF Author: Geoffrey Lawrence Booth
Publisher:
ISBN:
Category :
Languages : en
Pages :

Get Book

Book Description

Some aspects of the construction and implementation of error-correcting linear codes

Some aspects of the construction and implementation of error-correcting linear codes PDF Author: Geoffrey Lawrence Booth
Publisher:
ISBN:
Category :
Languages : en
Pages :

View

Book Description


List Decoding of Error-Correcting Codes

List Decoding of Error-Correcting Codes PDF Author: Venkatesan Guruswami
Publisher: Springer
ISBN: 3540301801
Category : Computers
Languages : en
Pages : 352

View

Book Description
How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of “error-correcting codes”. This theory has traditionally gone hand in hand with the algorithmic theory of “decoding” that tackles the problem of recovering from the errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof“list-decoding” can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or “encode”) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2.

Error-Correcting Linear Codes

Error-Correcting Linear Codes PDF Author: Anton Betten
Publisher: Springer Science & Business Media
ISBN: 3540317031
Category : Mathematics
Languages : en
Pages : 798

View

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.

Advances on Superelliptic Curves and Their Applications

Advances on Superelliptic Curves and Their Applications PDF Author: L. Beshaj
Publisher: IOS Press
ISBN: 1614995206
Category : Computers
Languages : en
Pages : 388

View

Book Description
This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.

Research in Progress

Research in Progress PDF Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages :

View

Book Description


Introduction to Coding Theory

Introduction to Coding Theory PDF Author: Jurgen Bierbrauer
Publisher: CRC Press
ISBN: 148229981X
Category : Computers
Languages : en
Pages : 512

View

Book Description
This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes PDF Author: Marc Fossorier
Publisher: Springer
ISBN: 3540448284
Category : Mathematics
Languages : en
Pages : 270

View

Book Description
This book constitutes the refereed proceedings of the 15th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-15, held in Toulouse, France, in May 2003.The 25 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 40 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.

ICT Innovations 2009

ICT Innovations 2009 PDF Author: Danco Davcev
Publisher: Springer Science & Business Media
ISBN: 3642107818
Category : Technology & Engineering
Languages : en
Pages : 462

View

Book Description
This book is the result of the first International Conference ICT Innovations 2009. The ICT Innovations conference is the primary scientific action of the Macedonian Society on Information and Communication Technologies (ICT-ACT). It promotes the publication of scientific results of the international community related to innovative fundamental and applied research in ICT. Today, ICT has enlarged its horizons and it is practiced under multidisciplinary contexts that introduce new challenges to theore- cal and technical approaches. The ICT Innovations 2009 conference gathered academics, professionals and pr- titioners reporting their valuable experiences in developing solutions and systems in the industrial and business arena especially innovative commercial implementations, novel applications of technology, and experience in applying recent research advances to practical situations, in any ICT areas. The conference focuses on issues concerning a variety of ICT fields like: • Multimedia Information Systems • Artificial Intelligence • Pervasive and Ubiquitous Computing • Eco and Bio Informatics • Internet and Web Applications and Services • Wireless and Mobile Communications and Services • Computer Networks, Security and Cryptography • Distributed Systems, GRID and Cloud Computing ICT Innovations 2009 Conference was held in Ohrid, Macedonia, in September 28-30, 2009. Local arrangements provided by the members of the Macedonian Society on Information and Communication Technologies – ICT-ACT, mainly consisting of teaching and research staff of Computer Science Department at Faculty of Electrical Engineering and Information Technologies and Institute of Informatics at Faculty of Natural Sciences, both at Ss. Cyril and Methodius University in Skopje, Macedonia.

Error-Correction Coding for Digital Communications

Error-Correction Coding for Digital Communications PDF Author: George C. Clark Jr.
Publisher: Springer Science & Business Media
ISBN: 1489921745
Category : Technology & Engineering
Languages : en
Pages : 422

View

Book Description
Error-correction coding is being used on an almost routine basis in most new communication systems. Not only is coding equipment being used to increase the energy efficiency of communication links, but coding ideas are also providing innovative solutions to many related communication problems. Among these are the elimination of intersymbol interference caused by filtering and multipath and the improved demodulation of certain frequency modulated signals by taking advantage of the "natural" coding provided by a continuous phase. Although several books and nu merous articles have been written on coding theory, there are still noticeable deficiencies. First, the practical aspects of translating a specific decoding algorithm into actual hardware have been largely ignored. The information that is available is sketchy and is widely dispersed. Second, the information required to evaluate a particular technique under situations that are en countered in practice is available for the most part only in private company reports. This book is aimed at correcting both of these problems. It is written for the design engineer who must build the coding and decoding equipment and for the communication system engineer who must incorporate this equipment into a system. It is also suitable as a senior-level or first-year graduate text for an introductory one-semester course in coding theory. The book U"Ses a minimum of mathematics and entirely avoids the classical theorem/proof approach that is often seen in coding texts.

The Amazing World of Quantum Computing

The Amazing World of Quantum Computing PDF Author: Rajendra K. Bera
Publisher: Springer Nature
ISBN: 9811524718
Category : Science
Languages : en
Pages : 265

View

Book Description
This book discusses the application of quantum mechanics to computing. It explains the fundamental concepts of quantum mechanics and then goes on to discuss various elements of mathematics required for quantum computing. Quantum cryptography, waves and Fourier analysis, measuring quantum systems, comparison to classical mechanics, quantum gates, and important algorithms in quantum computing are among the topics covered. The book offers a valuable resource for graduate and senior undergraduate students in STEM (science, technology, engineering, and mathematics) fields with an interest in designing quantum algorithms. Readers are expected to have a firm grasp of linear algebra and some familiarity with Fourier analysis.