Equations over Finite Fields PDF Download
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Author: W.M. Schmidt
Publisher: Springer
ISBN: 3540381236
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Author: W.M. Schmidt
Publisher: Springer
ISBN: 3540381236
Category : Mathematics
Languages : en
Pages : 277
Get Book Here
Book Description
Author: Wolfgang M. Schmidt
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Author: Carlos Moreno
Publisher: Cambridge University Press
ISBN: 9780521459013
Category : Mathematics
Languages : en
Pages : 264
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Book Description
Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.
Author: J. W. P. Hirschfeld
Publisher: Princeton University Press
ISBN: 1400847419
Category : Mathematics
Languages : en
Pages : 717
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Book Description
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
Author: Rudolf Lidl
Publisher: Cambridge University Press
ISBN: 9780521392310
Category : Mathematics
Languages : en
Pages : 784
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Book Description
This book is devoted entirely to the theory of finite fields.
Author: Gary L. Mullen
Publisher: CRC Press
ISBN: 1439873828
Category : Computers
Languages : en
Pages : 1048
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Book Description
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and
Author: László Rédei
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Author: David J. Covert
Publisher: American Mathematical Soc.
ISBN: 1470460319
Category : Education
Languages : en
Pages : 181
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Book Description
Erdős asked how many distinct distances must there be in a set of n n points in the plane. Falconer asked a continuous analogue, essentially asking what is the minimal Hausdorff dimension required of a compact set in order to guarantee that the set of distinct distances has positive Lebesgue measure in R R. The finite field distance problem poses the analogous question in a vector space over a finite field. The problem is relatively new but remains tantalizingly out of reach. This book provides an accessible, exciting summary of known results. The tools used range over combinatorics, number theory, analysis, and algebra. The intended audience is graduate students and advanced undergraduates interested in investigating the unknown dimensions of the problem. Results available until now only in the research literature are clearly explained and beautifully motivated. A concluding chapter opens up connections to related topics in combinatorics and number theory: incidence theory, sum-product phenomena, Waring's problem, and the Kakeya conjecture.
Author: Janet Simmons
Publisher: Nova Publishers
ISBN: 9781536104004
Category : Mathematics
Languages : en
Pages : 125
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Book Description
This book provides new research in finite fields. Chapter One presents some techniques that rely on a combination of results from graph theory, finite fields, matrix theory, and finite geometry to researchers working in the area of preserver problems. It also gives a brief presentation of this research field to other mathematicians. Chapter Two contains a basic and self-contained introduction to classical coherent state transforms, namely classical wavelet and classical wave-packet transforms, on finite fields. Chapter Three proposes an intrinsic representation of finite m? extension as this is a tradition for finite extension fields. Chapter Four reviews m? cyclic codes on a m? field. Chapter Five discusses two problems of Carlitz and their generalizations.
Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Category : Mathematics
Languages : en
Pages : 360
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Book Description
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.
