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Commutative Algebra Methods For Coding Theory

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Commutative Algebra Methods For Coding Theory

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Author : Ştefan Ovidiu I. Tohăneanu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-01

Commutative Algebra Methods For Coding Theory written by Ştefan Ovidiu I. Tohăneanu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.

This book aims to be a comprehensive treatise on the interactions between Coding Theory and Commutative Algebra. With the help of a multitude of examples, it expands and systematizes the known and versatile commutative algebraic framework used, since the early 90’s, to study linear codes. The book provides the necessary background for the reader to advance with similar research on coding theory topics from commutative algebraic perspectives.

Commutative Algebra Methods For Coding Theory

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Author : Ştefan Ovidiu I. Tohăneanu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-01

Commutative Algebra Methods For Coding Theory

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Author : Stefan Ovidiu Tohaneanu
language : en
Publisher:
Release Date : 2024-06-17

Commutative Algebra Methods For Coding Theory written by Stefan Ovidiu Tohaneanu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-17 with Mathematics categories.

This book aims to be a comprehensive treatise on the interactions between Coding Theory and Commutative Algebra. With the help of a multitude of examples, it expands and systematizes the known and versatile commutative algebraic framework used, since the early 90's, to study linear codes. The book provides the necessary background for the reader to advance with similar research on coding theory topics from commutative algebraic perspectives.

Using Algebraic Geometry

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Author : David A. Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Using Algebraic Geometry written by David A. Cox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gr"obner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

Coding Theory And Algebraic Geometry

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Author : Henning Stichtenoth
language : en
Publisher: Springer
Release Date : 2006-11-15

Coding Theory And Algebraic Geometry written by Henning Stichtenoth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

About ten years ago, V.D. Goppa found a surprising connection between the theory of algebraic curves over a finite field and error-correcting codes. The aim of the meeting "Algebraic Geometry and Coding Theory" was to give a survey on the present state of research in this field and related topics. The proceedings contain research papers on several aspects of the theory, among them: Codes constructed from special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen- tial sums, Fast multiplication in finite fields, Asymptotic number of points on algebraic curves, Sphere packings.

Computational Commutative Algebra 1

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Author : Martin Kreuzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-05

Computational Commutative Algebra 1 written by Martin Kreuzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-05 with Mathematics categories.

This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.

Computational Invariant Theory

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Author : Harm Derksen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Computational Invariant Theory written by Harm Derksen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Invariant theory is a subject with a long tradition and an astounding abil ity to rejuvenate itself whenever it reappears on the mathematical stage. Throughout the history of invariant theory, two features of it have always been at the center of attention: computation and applications. This book is about the computational aspects of invariant theory. We present algorithms for calculating the invariant ring of a group that is linearly reductive or fi nite, including the modular case. These algorithms form the central pillars around which the book is built. To prepare the ground for the algorithms, we present Grabner basis methods and some general theory of invariants. Moreover, the algorithms and their behavior depend heavily on structural properties of the invariant ring to be computed. Large parts of the book are devoted to studying such properties. Finally, most of the applications of in variant theory depend on the ability to calculate invariant rings. The last chapter of this book provides a sample of applications inside and outside of mathematics.

Gr Bner Bases Coding And Cryptography

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Author : Massimiliano Sala
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-28

Gr Bner Bases Coding And Cryptography written by Massimiliano Sala and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-28 with Mathematics categories.

Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations. This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.

Computational Algebra Course And Exercises With Solutions

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Author : Ihsen Yengui
language : en
Publisher: World Scientific
Release Date : 2021-05-17

Computational Algebra Course And Exercises With Solutions written by Ihsen Yengui and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-17 with Mathematics categories.

This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.

Harmonic Analysis Methods In Partial Differential Equations

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Author : Changxing Miao
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-06-02

Harmonic Analysis Methods In Partial Differential Equations written by Changxing Miao and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-02 with Mathematics categories.

This volume applies theories of harmonic analysis to the study of nonlinear partial differential equations. It covers consolidation characterizations of differentiable function spaces, and the theory of three generations of C-Z singular integral operators, Fourier restriction estimation, Strichartz estimation, and Littlewood-Paley theory. It combines harmonic analysis methods with the study of partial differential equations.

Commutative Algebra Methods For Coding Theory

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