Counting Polynomial Matrices Over Finite Fields

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Counting Polynomial Matrices over Finite Fields

Author : Julia Lieb
Publisher : BoD – Books on Demand
ISBN 13 : 3958260640
Total Pages : 166 pages
Book Rating : 4.9/5 (582 download)

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Book Synopsis Counting Polynomial Matrices over Finite Fields by : Julia Lieb

Download or read book Counting Polynomial Matrices over Finite Fields written by Julia Lieb and published by BoD – Books on Demand. This book was released on 2017-09-15 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory. Primeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transferred to criteria for non-catastrophicity of convolutional codes. In particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional code is non-catastrophic. Moreover, other networks of linear systems and convolutional codes are considered.

Topics in Galois Fields

Author : Dirk Hachenberger
Publisher : Springer Nature
ISBN 13 : 3030608069
Total Pages : 785 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Topics in Galois Fields by : Dirk Hachenberger

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.

2016 MATRIX Annals

Author : Jan de Gier
Publisher : Springer
ISBN 13 : 3319722999
Total Pages : 667 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis 2016 MATRIX Annals by : Jan de Gier

Download or read book 2016 MATRIX Annals written by Jan de Gier and published by Springer. This book was released on 2018-04-10 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.

Handbook of Finite Fields

Author : Gary L. Mullen
Publisher : CRC Press
ISBN 13 : 1439873828
Total Pages : 1048 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Handbook of Finite Fields by : Gary L. Mullen

Download or read book Handbook of Finite Fields written by Gary L. Mullen and published by CRC Press. This book was released on 2013-06-17 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Handbook of Linear Algebra, Second Edition

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1466507284
Total Pages : 1906 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Linear Algebra, Second Edition by : Leslie Hogben

Download or read book Handbook of Linear Algebra, Second Edition written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Finite Fields: Theory and Computation

Author : Igor Shparlinski
Publisher : Springer Science & Business Media
ISBN 13 : 940159239X
Total Pages : 532 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Finite Fields: Theory and Computation by : Igor Shparlinski

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.

Progress in Cryptology – AFRICACRYPT 2016

Author : David Pointcheval
Publisher : Springer
ISBN 13 : 331931517X
Total Pages : 370 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Progress in Cryptology – AFRICACRYPT 2016 by : David Pointcheval

Download or read book Progress in Cryptology – AFRICACRYPT 2016 written by David Pointcheval and published by Springer. This book was released on 2016-04-07 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the 8th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2016, held in Fes, Morooco, in April 2016. The 18 papers presented in this book were carefully reviewed and selected from 65 submissions. The aim of Africacrypt 2016 is to provide an international forum for practitioners and researchers from industry, academia and government from all over the world for a wide ranging discussion of all forms of cryptography. Topics of interest are such as lattices; elliptic curves; secret-key cryptanalysis; efficient implementations; secure protocols; and public-key cryptography.

Fundamentals of Computation Theory

Author : Adrian Kosowski
Publisher : Springer
ISBN 13 : 3319221779
Total Pages : 397 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Fundamentals of Computation Theory by : Adrian Kosowski

Download or read book Fundamentals of Computation Theory written by Adrian Kosowski and published by Springer. This book was released on 2015-08-03 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th International Symposium on Fundamentals of Computation Theory, FCT 2015, held in Gdańsk, Poland, in August 2015. The 27 revised full papers presented were carefully reviewed and selected from 60 submissions. The papers cover topics in three main areas: algorithms, formal methods, and emerging fields and are organized in topical sections on geometry, combinatorics, text algorithms; complexity and Boolean functions; languages; set algorithms, covering, and traversal; graph algorithms and networking applications; anonymity and indistinguishability; graphs, automata, and dynamics; and logic and games.

Progress in Cryptology – AFRICACRYPT 2018

Author : Antoine Joux
Publisher : Springer
ISBN 13 : 3319893394
Total Pages : 371 pages
Book Rating : 4.3/5 (198 download)

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Book Synopsis Progress in Cryptology – AFRICACRYPT 2018 by : Antoine Joux

Download or read book Progress in Cryptology – AFRICACRYPT 2018 written by Antoine Joux and published by Springer. This book was released on 2018-04-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2018, held in Marrakesh, Morocco, in May 2018. The 19 papers presented in this book were carefully reviewed and selected from 54 submissions. AFRICACRYPT is a major scientific event that seeks to advance and promote the field of cryptology on the African continent. The conference has systematically drawn some excellent contributions to the field. The conference has always been organized in cooperation with the International Association for Cryptologic Research (IACR).

Finite Fields and Applications

Author : Dieter Jungnickel
Publisher : Springer Science & Business Media
ISBN 13 : 9783540411093
Total Pages : 514 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Finite Fields and Applications by : Dieter Jungnickel

Download or read book Finite Fields and Applications written by Dieter Jungnickel and published by Springer Science & Business Media. This book was released on 2001-03-20 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re- quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci- nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.

Automata, Languages and Programming

Author : Peter Widmayer
Publisher : Springer
ISBN 13 : 3540454659
Total Pages : 1089 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Automata, Languages and Programming by : Peter Widmayer

Download or read book Automata, Languages and Programming written by Peter Widmayer and published by Springer. This book was released on 2003-08-03 with total page 1089 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 29th International Colloquium on Automata, Languages and Programming, ICALP 2002, held in Malaga, Spain, in July 2002.The 83 revised full papers presented together with 7 invited papers were carefully reviewed and selected from a total of 269 submissions. All current aspects of theoretical computer science are addressed and major new results are presented.

Arithmetic of Finite Fields

Author : Charles Small
Publisher : CRC Press
ISBN 13 : 9780824785260
Total Pages : 254 pages
Book Rating : 4.7/5 (852 download)

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Book Synopsis Arithmetic of Finite Fields by : Charles Small

Download or read book Arithmetic of Finite Fields written by Charles Small and published by CRC Press. This book was released on 1991-04-24 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Text for a one-semester course at the advanced undergraduate/beginning graduate level, or reference for algebraists and mathematicians interested in algebra, algebraic geometry, and number theory, examines counting or estimating numbers of solutions of equations in finite fields concentrating on top

Complexity Lower Bounds Using Linear Algebra

Author : Satyanarayana V. Lokam
Publisher : Now Publishers Inc
ISBN 13 : 1601982429
Total Pages : 177 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Complexity Lower Bounds Using Linear Algebra by : Satyanarayana V. Lokam

Download or read book Complexity Lower Bounds Using Linear Algebra written by Satyanarayana V. Lokam and published by Now Publishers Inc. This book was released on 2009-07-20 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: We survey several techniques for proving lower bounds in Boolean, algebraic, and communication complexity based on certain linear algebraic approaches. The common theme among these approaches is to study robustness measures of matrix rank that capture the complexity in a given model. Suitably strong lower bounds on such robustness functions of explicit matrices lead to important consequences in the corresponding circuit or communication models. Many of the linear algebraic problems arising from these approaches are independently interesting mathematical challenges.

Logic, Language, Information and Computation

Author : Wilfrid Hodges
Publisher : Springer
ISBN 13 : 3540699376
Total Pages : 321 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Logic, Language, Information and Computation by : Wilfrid Hodges

Download or read book Logic, Language, Information and Computation written by Wilfrid Hodges and published by Springer. This book was released on 2008-06-27 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the 4th volume of the FoLLI LNAI subline; containing the refereed proceedings of the 15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008, held in Edinburgh, UK, in July 2008. The 21 revised full papers presented together with the abstracts of 7 tutorials and invited lectures were carefully reviewed and selected from numerous submissions. The papers cover all pertinent subjects in computer science with particular interest in cross-disciplinary topics. Typical areas of interest are: foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions and resources; foundational aspects of information organization, search, flow, sharing, and protection.

2017 MATRIX Annals

Author : Jan de Gier
Publisher : Springer
ISBN 13 : 3030041611
Total Pages : 702 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis 2017 MATRIX Annals by : Jan de Gier

Download or read book 2017 MATRIX Annals written by Jan de Gier and published by Springer. This book was released on 2019-03-13 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in its second year, 2017: - Hypergeometric Motives and Calabi–Yau Differential Equations - Computational Inverse Problems - Integrability in Low-Dimensional Quantum Systems - Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book - Combinatorics, Statistical Mechanics, and Conformal Field Theory - Mathematics of Risk - Tutte Centenary Retreat - Geometric R-Matrices: from Geometry to Probability The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Advances in Cryptology – EUROCRYPT 2019

Author : Yuval Ishai
Publisher : Springer
ISBN 13 : 3030176533
Total Pages : 766 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Advances in Cryptology – EUROCRYPT 2019 by : Yuval Ishai

Download or read book Advances in Cryptology – EUROCRYPT 2019 written by Yuval Ishai and published by Springer. This book was released on 2019-05-14 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume-set LNCS 11476, 11477, and 11478 constitute the thoroughly refereed proceedings of the 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2019,held in Darmstadt, Germany, in May 2019. The 76 full papers presented were carefully reviewed and selected from 327 submissions. The papers are organized into the following topical sections: ABE and CCA security; succinct arguments and secure messaging; obfuscation; block ciphers; differential privacy; bounds for symmetric cryptography; non-malleability; blockchain and consensus; homomorphic primitives; standards; searchable encryption and ORAM; proofs of work and space; secure computation; quantum, secure computation and NIZK, lattice-based cryptography; foundations; efficient secure computation; signatures; information-theoretic cryptography; and cryptanalysis.

Bijective Combinatorics

Author : Nicholas Loehr
Publisher : CRC Press
ISBN 13 : 1439848866
Total Pages : 600 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Bijective Combinatorics by : Nicholas Loehr

Download or read book Bijective Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2011-02-10 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical