Galois Fields And Galois Rings Made Easy

Download Read Online Galois Fields And Galois Rings Made Easy book
Author: Maurice Kibler
Publisher: Elsevier
ISBN: 0081023510
Size: 25.80 MB
Format: PDF, ePub, Mobi
View: 6348

Galois Fields And Galois Rings Made Easy by Maurice Kibler


Original Title: Galois Fields And Galois Rings Made Easy

This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics. The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. Contains numerous examples that accompany the text Includes an important chapter on mutually unbiased bases Helps physicists and theoretical chemists understand this area of mathematics

Lectures On Finite Fields And Galois Rings

Download Read Online Lectures On Finite Fields And Galois Rings book
Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Size: 70.93 MB
Format: PDF, ePub
View: 3799

Lectures On Finite Fields And Galois Rings by Zhe-Xian Wan


Original Title: Lectures On Finite Fields And Galois Rings

This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.

Finite Fields And Galois Rings

Download Read Online Finite Fields And Galois Rings book
Author: Zhexian Wan
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814366342
Size: 16.84 MB
Format: PDF, Docs
View: 3481

Finite Fields And Galois Rings by Zhexian Wan


Original Title: Finite Fields And Galois Rings

Explicit construction and computation of finite fields are emphasized in this book. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is also provided.

Algebra

Download Read Online Algebra book
Author: Falko Lorenz
Publisher: Springer Science & Business Media
ISBN: 0387316086
Size: 16.26 MB
Format: PDF
View: 6432

Algebra by Falko Lorenz


Original Title: Algebra

This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.

Finite Commutative Rings And Their Applications

Download Read Online Finite Commutative Rings And Their Applications book
Author: Gilberto Bini
Publisher: Springer Science & Business Media
ISBN: 1461509572
Size: 21.10 MB
Format: PDF, Kindle
View: 6295

Finite Commutative Rings And Their Applications by Gilberto Bini


Original Title: Finite Commutative Rings And Their Applications

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Finite Fields And Applications

Download Read Online Finite Fields And Applications book
Author: Gary L. Mullen
Publisher: Springer Science & Business Media
ISBN: 3540213244
Size: 65.37 MB
Format: PDF, ePub, Mobi
View: 488

Finite Fields And Applications by Gary L. Mullen


Original Title: Finite Fields And Applications

This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004. The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.

Error Correcting Codes Over Galois Rings

Download Read Online Error Correcting Codes Over Galois Rings book
Author: Gregory Reid Holdman
Publisher:
ISBN:
Size: 53.85 MB
Format: PDF, Docs
View: 1613

Error Correcting Codes Over Galois Rings by Gregory Reid Holdman


Original Title: Error Correcting Codes Over Galois Rings

The theory of error-correcting codes has historically been most useful in the context of linear codes. Such codes may be viewed as vector spaces over Galois fields carrying with them many familiar and well-studied properties. A generalization of Galois fields is the concept of Galois rings. It is therefore natural to consider codes over Galois rings to study which properties such codes maintain in the move to a more general setting. This thesis will present two separate expositions on coding theory and Galois rings. After this, the intersection of these topics will be considered: codes over Galois rings.

Field And Galois Theory

Download Read Online Field And Galois Theory book
Author: Patrick Morandi
Publisher: Springer Science & Business Media
ISBN: 1461240409
Size: 65.11 MB
Format: PDF, Mobi
View: 2691

Field And Galois Theory by Patrick Morandi


Original Title: Field And Galois Theory

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.

Recent Books :