Characters And Cyclotomic Fields In Finite Geometry
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Characters And Cyclotomic Fields In Finite Geometry
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Author : Bernhard Schmidt
language : en
Publisher: Springer
Release Date : 2004-10-14
Characters And Cyclotomic Fields In Finite Geometry written by Bernhard Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-14 with Mathematics categories.
This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13
Finite Geometry And Character Theory
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Author : Alexander Pott
language : en
Publisher: Springer
Release Date : 2006-11-14
Finite Geometry And Character Theory written by Alexander Pott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.
Finite Geometry And Combinatorial Applications
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Author : Simeon Ball
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-02
Finite Geometry And Combinatorial Applications written by Simeon Ball and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-02 with Mathematics categories.
A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Finite Fields And Applications
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Author : Gary L. Mullen
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Finite Fields And Applications written by Gary L. Mullen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.
This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.
Arithmetic Of Finite Fields
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Author : Ferruh Özbudak
language : en
Publisher: Springer
Release Date : 2012-07-02
Arithmetic Of Finite Fields written by Ferruh Özbudak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-02 with Computers categories.
This book constitutes the refereed proceedings of the 4th International Workshop on the Arithmetic of Finite Field, WAIFI 2012, held in Bochum, Germany, in July 2012. The 13 revised full papers and 4 invited talks presented were carefully reviewed and selected from 29 submissions. The papers are organized in topical sections on coding theory and code-based cryptography, Boolean functions, finite field arithmetic, equations and functions, and polynomial factorization and permutation polynomial.
Arithmetic Of Finite Fields
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Author : Çetin Kaya Koç
language : en
Publisher: Springer
Release Date : 2015-02-21
Arithmetic Of Finite Fields written by Çetin Kaya Koç and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-21 with Computers categories.
This book constitutes the refereed proceedings of the 5th International Workshop on the Arithmetic of Finite Field, WAIFI 2014, held in Gebze, Turkey, in September 2014. The 9 revised full papers and 43 invited talks presented were carefully reviewed and selected from 27 submissions. This workshop is a forum of mathematicians, computer scientists, engineers and physicists performing research on finite field arithmetic, interested in communicating the advances in the theory, applications, and implementations of finite fields. The workshop will help to bridge the gap between the mathematical theory of finite fields and their hardware/software implementations and technical applications.
Introduction To Cyclotomic Fields
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Author : Lawrence C. Washington
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Introduction To Cyclotomic Fields written by Lawrence C. Washington 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 1997 with Mathematics categories.
This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.
Higher Dimensional Geometry Over Finite Fields
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Author : D. Kaledin
language : en
Publisher: IOS Press
Release Date : 2008-06-05
Higher Dimensional Geometry Over Finite Fields written by D. Kaledin and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-05 with Mathematics categories.
Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the most important such number systems, playing a vital role in military and civilian communications through coding theory and cryptography. These disciplines have evolved over recent decades, and where once the focus was on algebraic curves over finite fields, recent developments have revealed the increasing importance of higher-dimensional algebraic varieties over finite fields. The papers included in this publication introduce the reader to recent developments in algebraic geometry over finite fields with particular attention to applications of geometric techniques to the study of rational points on varieties over finite fields of dimension of at least 2.
Information Security Coding Theory And Related Combinatorics
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Author : Dean Crnković
language : en
Publisher: IOS Press
Release Date : 2011
Information Security Coding Theory And Related Combinatorics written by Dean Crnković and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Computers categories.
"Published in cooperation with NATO Emerging Security Challenges Division"--T.p.
Topics In Galois Fields
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Author : Dirk Hachenberger
language : en
Publisher: Springer Nature
Release Date : 2020-09-29
Topics In Galois Fields written by Dirk Hachenberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-29 with Mathematics categories.
This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.