Galois Fields Linear Feedback Shift Registers and Their Applications

• Author : Ulrich Jetzek
• Publisher : Unknown
• Release : 01 July 2018

This book gives an excellent introduction to finite groups and fields as well as their applications. Readers learn to understand and use galois fields and their relationship with linear feedback shift registers. The book has a strong focus on the technical application of galois fields, such as navigation systems and cryptography.

• Author : Pascale Charpin,Alexander Pott,Arne Winterhof
• Publisher : Walter de Gruyter
• Release : 28 May 2013

This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in

• Author : Tamara Radivilova,Dmytro Ageyev,Natalia Kryvinska
• Publisher : Springer Nature
• Release : 20 June 2020

This book addresses the challenges and opportunities of information/data processing and management. It also covers a range of methods, techniques and strategies for making it more efficient, approaches to increasing its usage, and ways to minimize information/data loss while improving customer satisfaction. Information and Communication Technologies (ICTs) and the Service Systems associated with them have had an enormous impact on businesses and our day-to-day lives over the past three decades, and continue to do so. This development has

• Author : Tor Helleseth,Dilip Sarwate,Hong-Yeop Song,Kyeongcheol Yang
• Publisher : Springer Science & Business Media
• Release : 01 June 2005

This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Sequences and Their Applications, SETA 2004, held in Seoul, Korea in October 2004. The 30 revised full papers presented together with 4 invited survey articles were carefully selected during two rounds of reviewing and improvement from initially 59 submissions. The papers are organized in topical sections on complexity of sequences, perfect sequences, sequence construction, sequences modulo z, sequence generator properties and applications, multi-dimensional sequences, optics and OFDM applications, and polynomials and functions.

• Author : International Conference on Finite Fields and Applications,Gary L. Mullen,INTERNATIONAL CONFERENCE ON FINITE FIELD,Alain Poli
• Publisher : Springer Science & Business Media
• Release : 19 March 2004

This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004. The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.

• Author : Harald Niederreiter,Alina Ostafe,Daniel Panario,Arne Winterhof
• Publisher : Walter de Gruyter GmbH & Co KG
• Release : 20 August 2014

Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking,

• Author : Ignacio Luengo
• Publisher : American Mathematical Soc.
• Release : 15 January 2009

This volume contains articles representing the courses given at the 2005 RSME Santalo Summer School on ``Recent Trends in Cryptography''. The main goal of the Summer School was to present some of the recent mathematical methods used in cryptography and cryptanalysis. The School was oriented to graduate and doctoral students, as well as recent doctorates. The material is presented in an expository manner with many examples and references. The topics in this volume cover some of the most interesting new developments

• Author : James A. Davis
• Publisher : Walter de Gruyter GmbH & Co KG
• Release : 26 October 2020

The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.

• Author : Dirk Hachenberger,Dieter Jungnickel
• Publisher : Springer Nature
• Release : 29 September 2020

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

• Author : Frank Fitzek,Fabrizio Granelli,Patrick Seeling
• Publisher : Academic Press
• Release : 20 May 2020

Computing in Communication Networks: From Theory to Practice provides comprehensive details and practical implementation tactics on the novel concepts and enabling technologies at the core of the paradigm shift from store and forward (dumb) to compute and forward (intelligent) in future communication networks and systems. The book explains how to create virtualized large scale testbeds using well-established open source software, such as Mininet and Docker. It shows how and where to place disruptive techniques, such as machine learning, compressed sensing,

• Author : Theodore Simos
• Publisher : CRC Press
• Release : 20 May 2019

The aim of IeCCS 2005, which was held in May 2005, was to bring together leading scientists of the international Computer Science community and to attract original research papers. This volume in the Lecture Series on Computer and Computational Sciences contains the extended abstracts of the presentations. The topics covered included (but were not limited to): Numerical Analysis, Scientific Computation, Computational Mathematics, Mathematical Software, Programming Techniques and Languages, Parallel Algorithms and its Applications, Symbolic and Algebraic Manipulation, Analysis of Algorithms, Problem Complexity,

• Author : Rudolf Lidl,Harald Niederreiter
• Publisher : Cambridge University Press
• Release : 21 July 1994

Presents an introduction to the theory of finite fields and some of its most important applications.

• Author : Bruce Watson,Derick Wood
• Publisher : Springer Science & Business Media
• Release : 16 January 2003

TheCIAAconferenceseriesprovidesaforumforthenewproblemsand challenges. Intheseconferences,boththeoreticalandpracticalresultsrelatedto theapplicationandimplementationofautomatawerepresentedanddiscussed, andsoftwarepackagesandtoolkitsweredemonstrated. Theparticipantsofthe conferenceserieswerefrombothresearchinstitutionsandindustry. Wethankalloftheprogramcommitteemembersandrefereesfortheire?orts inrefereeingandselectingpapers. Thisvolumewaseditedwithmuchhelpfrom NanetteSaesandHannekeDriever,whiletheconferenceitselfwasrunsmoothly withthehelpofElmarieWillemse,NanetteSaes,andTheoKoopman. VI Foreword WealsowishtothanktheSouthAfricanNRF(forfundingairfares)andthe DepartmentofComputerScience,UniversityofPretoria,fortheir?nancialand logisticsupportoftheconference. WealsothanktheeditorsoftheLectureNotes inComputerScienceseriesandSpringer-Verlag,inparticularAnnaKramer,for theirhelpinpublishingthisvolume. October2002 BruceW. Watson DerickWood CIAA 2001 Program Committee BernardBoigelot Universit´edeLiege,Belgium Jean-MarcChamparnaud Universit´edeRouen,France MaximeCrochemore UniversityofMarne-la-Vall´ee,France OscarIbarra UniversityofCaliforniaatSantaBarbara,USA LauriKarttunen XeroxPaloAltoResearchCenter,USA NilsKlarlund AT&TLaboratories,USA DenisMaurel Universit´edeTours,France MehryarMohri AT&TLaboratories,USA Jean-EricPin Universit´eParis7,France KaiSalomaa Queen'sUniversity,Canada HelmutSeidl TrierUniversity,Germany BruceWatson(

• Author : Yves Aubry,Christophe Ritzenthaler,Alexey Zykin
• Publisher : American Mathematical Soc.
• Release : 16 May 2022

This volume contains the proceedings of the 13th $\mathrm{AGC^2T}$ conference, held March 14-18, 2011, in Marseille, France, together with the proceedings of the 2011 Geocrypt conference, held June 19-24, 2011, in Bastia, France. The original research articles contained in this volume cover various topics ranging from algebraic number theory to Diophantine geometry, curves and abelian varieties over finite fields and applications to codes, boolean functions or cryptography. The international conference $\mathrm{AGC^2T}$, which is held every two years in Marseille,

• Author : Rudolf Lidl,Harald Niederreiter
• Publisher : Cambridge University Press
• Release : 16 May 1997

This book is devoted entirely to the theory of finite fields.