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ISBN 13 : 9781665402873
Total Pages : pages
Book Rating : 4.4/5 (28 download)
Download or read book 2020 Algebraic and Combinatorial Coding Theory (ACCT) written by and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 191 pages
Book Rating : 4.:/5 (897 download)
Download or read book Algebraic and Combinatorial Coding Theory written by and published by . This book was released on 1988 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic and Combinatorial Coding Theory written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ian F. Blake
Publisher : Academic Press
ISBN 13 : 1483260291
Total Pages : 244 pages
Book Rating : 4.4/5 (832 download)
Download or read book An Introduction to Algebraic and Combinatorial Coding Theory written by Ian F. Blake and published by Academic Press. This book was released on 2014-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Algebraic and Combinatorial Coding Theory focuses on the principles, operations, and approaches involved in the combinatorial coding theory, including linear transformations, chain groups, vector spaces, and combinatorial constructions. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on quadratic residues and codes, self-dual and quasicyclic codes, balanced incomplete block designs and codes, polynomial approach to coding, and linear transformations of vector spaces over finite fields. The text then examines coding and combinatorics, including chains and chain groups, equidistant codes, matroids, graphs, and coding, matroids, and dual chain groups. The manuscript also ponders on Möbius inversion formula, Lucas's theorem, and Mathieu groups. The publication is a valuable source of information for mathematicians and researchers interested in the combinatorial coding theory.
Download or read book Fourth International Workshop Algebraic and Combinatorial Coding Theory written by and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (897 download)
Download or read book Algebraic and Combinatorial Coding Theory written by and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Olga Moreira
Publisher :
ISBN 13 : 9781774698310
Total Pages : 0 pages
Book Rating : 4.6/5 (983 download)
Download or read book An Introduction to Algebraic and Combinatorial Coding Theory written by Olga Moreira and published by . This book was released on 2023-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An Introduction to Algebraic and Combinatorial Coding Theory" is a comprehensive book that offers a thorough exploration of the principles and techniques of coding theory. It serves as a valuable resource for readers interested in gaining a deeper understanding of error detection and correction in communication systems. With its well-structured chapters covering coding theory fundamentals, algebraic codes, cyclic codes, block codes, and advanced coding techniques, this book caters to the needs of students, researchers, and professionals in the field. It provides a solid foundation in coding theory and showcases its practical applications in various domains, including telecommunications, data storage, and cryptography.
Author :
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ISBN 13 :
Total Pages : 191 pages
Book Rating : 4.:/5 (229 download)
Download or read book Proceedings written by and published by . This book was released on 1988 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dijen Ray-Chaudhuri
Publisher : Springer Science & Business Media
ISBN 13 : 1461389941
Total Pages : 252 pages
Book Rating : 4.4/5 (613 download)
Download or read book Coding Theory and Design Theory written by Dijen Ray-Chaudhuri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for organizing a workshop which brought together many of the major figures in a variety of research fields in which coding theory and design theory are used. A vner Friedman Willard Miller, Jr. PREFACE Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 pa per of Reverand T. P. Kirkman "On a problem of Combinatorics", Cambridge and Dublin Math. Journal. The great Statistician R. A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of alge braic structures for construction of 2-designs (balanced incomplete block designs) can be found in R. C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs". Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper "Mathematical theory of the symmetrical factorial designs".
Author : Steven T. Dougherty
Publisher : Springer
ISBN 13 : 3319598066
Total Pages : 109 pages
Book Rating : 4.3/5 (195 download)
Download or read book Algebraic Coding Theory Over Finite Commutative Rings written by Steven T. Dougherty and published by Springer. This book was released on 2017-07-04 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.
Author : Simeon Ball
Publisher : Springer Nature
ISBN 13 : 3030411532
Total Pages : 185 pages
Book Rating : 4.0/5 (34 download)
Download or read book A Course in Algebraic Error-Correcting Codes written by Simeon Ball and published by Springer Nature. This book was released on 2020-05-08 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.
Author : François Boulier
Publisher : Springer Nature
ISBN 13 : 3030851656
Total Pages : 485 pages
Book Rating : 4.0/5 (38 download)
Download or read book Computer Algebra in Scientific Computing written by François Boulier and published by Springer Nature. This book was released on 2021-08-16 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 23rd International Workshop on Computer Algebra in Scientific Computing, CASC 2021, held in Sochi, Russia, in September 2021. The 24 full papers presented together with 1 invited talk were carefully reviewed and selected from 40 submissions. The papers cover theoretical computer algebra and its applications in scientific computing.
Author : Tzuong-tsieng Moh
Publisher : World Scientific
ISBN 13 : 9811220980
Total Pages : 266 pages
Book Rating : 4.8/5 (112 download)
Download or read book Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh and published by World Scientific. This book was released on 2022-02-18 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.
Author : Dijen Ray-Chaudhuri
Publisher : Springer
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.3/5 (91 download)
Download or read book Coding Theory and Design Theory written by Dijen Ray-Chaudhuri and published by Springer. This book was released on 1990-04-02 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for organizing a workshop which brought together many of the major figures in a variety of research fields in which coding theory and design theory are used. A vner Friedman Willard Miller, Jr. PREFACE Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 pa per of Reverand T. P. Kirkman "On a problem of Combinatorics", Cambridge and Dublin Math. Journal. The great Statistician R. A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of alge braic structures for construction of 2-designs (balanced incomplete block designs) can be found in R. C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs". Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper "Mathematical theory of the symmetrical factorial designs".
Author : Volodia Blinovsky
Publisher : Springer Science & Business Media
ISBN 13 : 1461561930
Total Pages : 116 pages
Book Rating : 4.4/5 (615 download)
Download or read book Asymptotic Combinatorial Coding Theory written by Volodia Blinovsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Combinatorial Coding Theory is devoted to the investigation of the combinatorial properties of transmission systems using discrete signals. The book presents results of interest to specialists in combinatorics seeking to apply combinatorial methods to problems of combinatorial coding theory. Asymptotic Combinatorial Coding Theory serves as an excellent reference for resarchers in discrete mathematics, combinatorics, and combinatorial coding theory, and may be used as a text for advanced courses on the subject.
Author : Ian F. Blake
Publisher : Academic Press
ISBN 13 : 1483260593
Total Pages : 369 pages
Book Rating : 4.4/5 (832 download)
Download or read book The Mathematical Theory of Coding written by Ian F. Blake and published by Academic Press. This book was released on 2014-05-10 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.
Author : J. H. van Lint
Publisher : Springer
ISBN 13 : 3540366571
Total Pages : 146 pages
Book Rating : 4.5/5 (43 download)
Download or read book Coding Theory written by J. H. van Lint and published by Springer. This book was released on 2009-08-14 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of Technology. The students who took the course were mathematics seniors and graduate students. Therefore a thorough knowledge of algebra. (a. o. linear algebra, theory of finite fields, characters of abelian groups) and also probability theory were assumed. After introducing coding theory and linear codes these notes concern topics mostly from algebraic coding theory. The practical side of the subject, e. g. circuitry, is not included. Some topics which one would like to include 1n a course for students of mathematics such as bounds on the information rate of codes and many connections between combinatorial mathematics and coding theory could not be treated due to lack of time. For an extension of the course into a third term these two topics would have been chosen. Although the material for this course came from many sources there are three which contributed heavily and which were used as suggested reading material for the students. These are W. W. Peterson's Error-Correcting Codes «(15]), E. R. Berlekamp's Algebraic Coding Theory «(5]) and several of the AFCRL-reports by E. F. Assmus, H. F. Mattson and R. Turyn ([2], (3), [4] a. o. ). For several fruitful discussions I would like to thank R. J. McEliece.
