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Author: G. Cohen Publisher: Elsevier ISBN: 0080530079 Category : Mathematics Languages : en Pages : 565
Book Description
The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems.Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer.A number of unsolved problems suitable for research projects are also discussed.
Author: G. Cohen Publisher: Elsevier ISBN: 0080530079 Category : Mathematics Languages : en Pages : 565
Book Description
The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems.Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer.A number of unsolved problems suitable for research projects are also discussed.
Author: Liqun Chen Publisher: Springer ISBN: 3642255167 Category : Computers Languages : en Pages : 508
Book Description
This book constitutes the refereed proceedings of the 13th IMA International Conference on Cryptography and Coding, IMACC 2011, held in Oxford, UK in December 2011. The 27 revised full papers presented together with one invited contribution were carefully reviewed and selected from 57 submissions. The papers cover a wide range of topics in the field of mathematics and computer science, including coding theory, homomorphic encryption, symmetric and public key cryptosystems, cryptographic functions and protocols, efficient pairing and scalar multiplication implementation, knowledge proof, and security analysis.
Author: Gerard Cohen Publisher: Springer Science & Business Media ISBN: 9783540551300 Category : Computers Languages : en Pages : 178
Book Description
This volume presents the proceedings of the first French-Soviet workshop on algebraic coding, held in Paris in July 1991. The idea for the workshop, born in Leningrad (now St. Petersburg) in 1990, was to bring together some of the best Soviet coding theorists. Scientists from France, Finland, Germany, Israel, Italy, Spain, and the United States also attended. The papers in the volume fall rather naturally into four categories: - Applications of exponential sums - Covering radius - Constructions -Decoding.
Author: Dijen Ray-Chaudhuri Publisher: Springer Science & Business Media ISBN: 1461389941 Category : Mathematics Languages : en Pages : 252
Book Description
This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for organizing a workshop which brought together many of the major figures in a variety of research fields in which coding theory and design theory are used. A vner Friedman Willard Miller, Jr. PREFACE Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 pa per of Reverand T. P. Kirkman "On a problem of Combinatorics", Cambridge and Dublin Math. Journal. The great Statistician R. A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of alge braic structures for construction of 2-designs (balanced incomplete block designs) can be found in R. C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs". Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper "Mathematical theory of the symmetrical factorial designs".
Author: Teo Mora Publisher: Springer Science & Business Media ISBN: 9783540510833 Category : Computers Languages : en Pages : 496
Book Description
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.
Author: Llorenc Huguet Publisher: Springer Science & Business Media ISBN: 9783540510826 Category : Computers Languages : en Pages : 428
Book Description
The present volume contains the proceedings of the AAECC-5 Conference held at Menorca (Balearic Islands), June 15-19, 1987. The annual International AAECC Conference covers a range of topics related to Applied Algebra, Error-Correcting Codes, Finite Algebraic Structures, Computational Methods and Complexity in Algebra and Geometry. For the AAECC-5 Conference 73 papers were presented. Out of these thirty papers were selected for publication in the proceedings. They deal with topics such as error correcting codes (concerning problems of covering radius, decoding methods, expert systems and general results in coding theory), computational algebra, Gröbner basis, complexity, finite algebra and graphs. The proceedings of the 6th conference are published as Vol. 357 of the Lecture Notes in Computer Science.
Author: Jurgen Bierbrauer Publisher: CRC Press ISBN: 135198960X Category : Mathematics Languages : en Pages : 318
Book Description
Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, and the geometric desciption of codes. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed. Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, Introduction to Coding Theory explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.
Author: Petteri Kaski Publisher: Springer Science & Business Media ISBN: 3540289917 Category : Mathematics Languages : en Pages : 415
Book Description
A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classi?cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation.
Author: Tuvi Etzion Publisher: World Scientific ISBN: 981125589X Category : Mathematics Languages : en Pages : 436
Book Description
In this monograph, we develop the theory of one of the most fascinating topics in coding theory, namely, perfect codes and related structures. Perfect codes are considered to be the most beautiful structure in coding theory, at least from the mathematical side. These codes are the largest ones with their given parameters. The book develops the theory of these codes in various metrics — Hamming, Johnson, Lee, Grassmann, as well as in other spaces and metrics. It also covers other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tilings, combinatorial designs, and more. The goal is to give the aspects of all these codes, to derive bounds on their sizes, and present various constructions for these codes.The intention is to offer a different perspective for the area of perfect codes. For example, in many chapters there is a section devoted to diameter perfect codes. In these codes, anticodes are used instead of balls and these anticodes are related to intersecting families, an area that is part of extremal combinatorics. This is one example that shows how we direct our exposition in this book to both researchers in coding theory and mathematicians interested in combinatorics and extremal combinatorics. New perspectives for MDS codes, different from the classic ones, which lead to new directions of research on these codes are another example of how this book may appeal to both researchers in coding theory and mathematicians.The book can also be used as a textbook, either on basic course in combinatorial coding theory, or as an advance course in combinatorial coding theory.
Author: G. Cohen
Author: G. Cohen
Author: Liqun Chen
Author: Gerard Cohen
Author: 
Author: Dijen Ray-Chaudhuri
Author: Teo Mora
Author: Llorenc Huguet
Author: Jurgen Bierbrauer
Author: Petteri Kaski
Author: Tuvi Etzion