Codes On Algebraic Curves

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
ISBN 13 : 9780306461446
Total Pages : 372 pages
Book Rating : 4.47/5 ( download)

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Download or read book Codes on Algebraic Curves written by Serguei A. Stepanov and published by Springer Science & Business Media. This book was released on 1999-07-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
ISBN 13 : 1461547857
Total Pages : 352 pages
Book Rating : 4.53/5 ( download)

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Download or read book Codes on Algebraic Curves written by Serguei A. Stepanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.

Author : Oliver Pretzel
Publisher : Clarendon Press
ISBN 13 : 0191589047
Total Pages : 209 pages
Book Rating : 4.41/5 ( download)

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Download or read book Codes and Algebraic Curves written by Oliver Pretzel and published by Clarendon Press. This book was released on 1998-01-08 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is an updated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, and applications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.

Author : Vera Pless
Publisher : North Holland
ISBN 13 :
Total Pages : 1220 pages
Book Rating : 4.52/5 ( download)

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Download or read book Handbook of Coding Theory written by Vera Pless and published by North Holland. This book was released on 1998-11-16 with total page 1220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : San Ling
Publisher : CRC Press
ISBN 13 : 1420079476
Total Pages : 340 pages
Book Rating : 4.70/5 ( download)

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Download or read book Algebraic Curves in Cryptography written by San Ling and published by CRC Press. This book was released on 2013-06-13 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sh

Author : Henning Stichtenoth
Publisher : Springer Science & Business Media
ISBN 13 : 3540768785
Total Pages : 360 pages
Book Rating : 4.84/5 ( download)

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Download or read book Algebraic Function Fields and Codes written by Henning Stichtenoth and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.

Author : M. Tsfasman
Publisher : Springer Science & Business Media
ISBN 13 : 9401138109
Total Pages : 671 pages
Book Rating : 4.09/5 ( download)

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Download or read book Algebraic-Geometric Codes written by M. Tsfasman and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.

Author : Judy L. Walker
Publisher : American Mathematical Soc.
ISBN 13 : 082182628X
Total Pages : 82 pages
Book Rating : 4.87/5 ( download)

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Download or read book Codes and Curves written by Judy L. Walker and published by American Mathematical Soc.. This book was released on 2000 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above it discussed."--BOOK JACKET.

Author : Goppa
Publisher : Springer Science & Business Media
ISBN 13 : 9401568707
Total Pages : 166 pages
Book Rating : 4.08/5 ( download)

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Download or read book Geometry and Codes written by Goppa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day. that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering: and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : Carlos Moreno
Publisher : Cambridge University Press
ISBN 13 : 9780521459013
Total Pages : 264 pages
Book Rating : 4.1X/5 ( download)

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Download or read book Algebraic Curves Over Finite Fields written by Carlos Moreno and published by Cambridge University Press. This book was released on 1993-10-14 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.