Download or read book The Number of Zeros of Linear Recurring Sequences Over Finite Fields written by Suwanda Hennedige Yasanthi Kottegoda and published by . This book was released on 2014 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, I discuss bounds for the set of possible number of zeros of a homogeneous linear recurring sequence over a finite field of q elements, based on an irreducible minimal polynomials of degree d and order m as the characteristic polynomial. I prove upper and lower bounds on the cardinality of the set of number of zeros. The set is determined when t = ( qd - 1)/m has the form q a + 1 or q2 a - qa + 1 where a is a positive integer. The connection with coding theory is a key ingredient. Also it is proved that the upper bound defined here is the best bound for the cardinality of the set of zeros, in the sense that it is reached infinitely often.
Download or read book The Number of Zeros of Linear Recurring Sequences Over Finite Fields written by Suwanda Hennedige Yasanthi Kottegoda (‡e author) and published by . This book was released on 2014 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, I discuss bounds for the set of possible number of zeros of a homogeneous linear recurring sequence over a finite field of q elements, based on an irreducible minimal polynomials of degree d and order m as the characteristic polynomial. I prove upper and lower bounds on the cardinality of the set of number of zeros. The set is determined when t = ( qd - 1)/m has the form q a + 1 or q2 a - qa + 1 where a is a positive integer. The connection with coding theory is a key ingredient. Also it is proved that the upper bound defined here is the best bound for the cardinality of the set of zeros, in the sense that it is reached infinitely often.
Download or read book Linear Recurring Sequences Over Finite Fields written by Robert J. McEliece and published by . This book was released on 1967 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Fields Theory and Computation written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.
Download or read book Computational and Algorithmic Problems in Finite Fields written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
Download or read book Recurrence Sequences written by Graham Everest and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
Download or read book Surveys in Combinatorics 2015 written by Artur Czumaj and published by Cambridge University Press. This book was released on 2015-07-02 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nine survey articles based on the invited lectures given at the 25th British Combinatorial Conference, held at the University of Warwick in July 2015. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, Ramsey theory, combinatorial geometry and curves over finite fields. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.
Download or read book Zeros and Asymptotics of Holonomic Sequences written by Rob Noble and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytic and Probabilistic Methods in Number Theory written by F. Schweiger and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Analytic and Probabilistic Methods in Number Theory".
Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Download or read book Algebraic Shift Register Sequences written by Mark Goresky and published by Cambridge University Press. This book was released on 2012-02-02 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the design, mathematical analysis and implementation of pseudo-random sequences for applications in communications, cryptography and simulations.
Download or read book Boolean Functions for Cryptography and Coding Theory written by Claude Carlet and published by Cambridge University Press. This book was released on 2021-01-07 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications.
Download or read book Combinatorics and Finite Fields written by Kai-Uwe Schmidt and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.
Download or read book Applied Algebra Algebraic Algorithms and Error Correcting Codes written by Marc Fossorier and published by Springer. This book was released on 2003-07-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999. The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.
Download or read book Algebraic Combinatorics written by Richard P. Stanley and published by Springer Science & Business Media. This book was released on 2013-06-17 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Download or read book Applied Algebra Algebraic Algorithms and Error correcting Codes written by Teo Mora and published by Springer Science & Business Media. This book was released on 1989-05-23 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988, for the first time, the two international conferences AAECC-6 and ISSAC'88 (International Symposium on Symbolic and Algebraic Computation, see Lecture Notes in Computer Science 358) have taken place as a Joint Conference in Rome, July 4-8, 1988. The topics of the two conferences are in fact widely related to each other and the Joint Conference presented a good occasion for the two research communities to meet and share scientific experiences and results. The proceedings of the AAECC-6 are included in this volume. The main topics are: Applied Algebra, Theory and Application of Error-Correcting Codes, Cryptography, Complexity, Algebra Based Methods and Applications in Symbolic Computing and Computer Algebra, and Algebraic Methods and Applications for Advanced Information Processing. Twelve invited papers on subjects of common interest for the two conferences are divided between this volume and the succeeding Lecture Notes volume devoted to ISSACC'88. The proceedings of the 5th conference are published as Vol. 356 of the Lecture Notes in Computer Science.
