Download or read book Characters and Cyclotomic Fields in Finite Geometry written by Bernhard Schmidt and published by Springer. This book was released on 2004-10-14 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Finite Geometry and Combinatorial Applications written by Simeon Ball and published by Cambridge University Press. This book was released on 2015-07-02 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

Download or read book Finite Fields and Applications written by Gary L. Mullen and published by American Mathematical Soc.. This book was released on 2008 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Arithmetic of Finite Fields written by Ferruh Özbudak and published by Springer. This book was released on 2012-07-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Finite Geometry and Character Theory written by Alexander Pott and published by Springer. This book was released on 2006-11-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Arithmetic of Finite Fields written by Çetin Kaya Koç and published by Springer. This book was released on 2015-02-21 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Information Security Coding Theory and Related Combinatorics written by Dean Crnković and published by IOS Press. This book was released on 2011 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Published in cooperation with NATO Emerging Security Challenges Division"--T.p.

Download or read book Topics in Galois Fields written by Dirk Hachenberger and published by Springer Nature. This book was released on 2020-09-29 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book New Advances in Designs Codes and Cryptography written by Charles J. Colbourn and published by Springer Nature. This book was released on with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometric Properties of Banach Spaces and Nonlinear Iterations written by Charles Chidume and published by Springer. This book was released on 2008-12-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

Download or read book Information Geometry written by and published by Springer Science & Business Media. This book was released on 2021 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sequences and Their Applications SETA 2010 written by Claude Carlet and published by Springer Science & Business Media. This book was released on 2010-09 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volumecontainstherefereedproceedingsoftheSixth International Conf- ence on Sequences and Their Applications (SETA 2010), held in Paris, France, September 13-17, 2010. The previous ?ve conferences were held in Singapore (RepublicofSingapore),Bergen(Norway),Seoul(SouthKorea),Beijing(China) and Lexington (USA). Topics of SETA include: – Randomness of sequences – Correlation (periodic and aperiodic types) and combinatorial aspects of - quences (di?erence sets) – Sequences with applications in coding theory and cryptography – Sequences over ?nite ?elds/rings/function ?elds – Linear and nonlinear feedback shift register sequences – Sequences for radar distance ranging, synchronization, identi?cation, and hardware testing – Sequences for wireless communication – Pseudorandom sequence generators – Boolean and vectorial functions for sequences, coding and/or cryptography – Multidimensional sequences and their correlation properties – Linear and nonlinear complexity of sequences The Technical Program Committee of SETA 2010 refereed 56 submitted - pers. Each paper was reviewed by at least 2 referees (at least 3 when an author was a TPC member) and the TPC selected 33 papers to be presented at the conference. In addition, we had 4 invited papers, byRobert Calderbank(Prin- ton University, USA), James Massey (retired from ETH Zurich, Switzerland), Jong-Seon No (Seoul National University, South Korea) and Arne Winterhof ¨ (Osterreichische Akademie der Wissenschaften, Austria). TheCo-chairsoftheTPCwereClaudeCarlet(Universit´ eParis8,France)and Alexander Pott (Otto-von-Guericke-Universit¨ at, Magdeburg, Germany). They wish to thank the other members of the ProgramCommittee: Thierry P.

Download or read book Geometric Analysis and PDEs written by Matthew J. Gursky and published by Springer. This book was released on 2009-07-31 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

Download or read book Singular Coverings of Toposes written by Marta Bunge and published by Springer. This book was released on 2007-01-19 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a self-contained theory of certain singular coverings of toposes, including branched coverings. This book is distinguished from classical treatments of the subject by its unexpected connection with a topic from functional analysis, namely, distributions. Although primarily aimed at topos theorists, this book may also be used as a textbook for advanced graduate courses introducing topos theory with an emphasis on geometric applications.

Download or read book Existence and Regularity Properties of the Integrated Density of States of Random Schr dinger Operators written by Ivan Veselic and published by Springer Science & Business Media. This book was released on 2008-01-02 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.

Download or read book Algebraic Design Theory written by Warwick De Launey and published by American Mathematical Soc.. This book was released on 2011 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro.